Exploratory Data Analysis

library(readr)
cancer <- read_csv("/Users/batul/Desktop/MVA/LUNGCANCER3.csv")
## Rows: 309 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (18): LUNG_CANCER, GENDER, AGE, SMOKING, YELLOW_FINGERS, ANXIETY, PEER_P...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
str(cancer)
## spc_tbl_ [309 × 18] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ LUNG_CANCER          : num [1:309] 1 1 0 0 0 1 1 1 0 1 ...
##  $ GENDER               : num [1:309] 0 0 1 0 1 1 0 1 1 0 ...
##  $ AGE                  : num [1:309] 69 74 59 63 63 75 52 51 68 53 ...
##  $ SMOKING              : num [1:309] 1 0 1 0 1 1 0 0 0 0 ...
##  $ YELLOW_FINGERS       : num [1:309] 1 0 0 1 1 1 0 1 0 1 ...
##  $ ANXIETY              : num [1:309] 1 0 0 1 0 0 0 1 1 1 ...
##  $ PEER_PRESSURE        : num [1:309] 0 0 1 0 0 0 0 1 0 1 ...
##  $ CHRONIC_DISEASE      : num [1:309] 0 1 0 0 0 1 0 0 0 1 ...
##  $ FATIGUE              : num [1:309] 1 1 1 0 0 1 1 1 1 0 ...
##  $ ALLERGY              : num [1:309] 0 1 0 0 0 1 0 1 0 1 ...
##  $ WHEEZING             : num [1:309] 1 0 1 0 1 1 1 0 0 0 ...
##  $ ALCOHOL_CONSUMING    : num [1:309] 1 0 0 1 0 0 1 0 0 1 ...
##  $ COUGHING             : num [1:309] 1 0 1 0 1 1 1 0 0 0 ...
##  $ SHORTNESS_OF_BREATH  : num [1:309] 1 1 1 0 1 1 1 1 0 0 ...
##  $ SWALLOWING_DIFFICULTY: num [1:309] 1 1 0 1 0 0 0 1 0 1 ...
##  $ CHEST_PAIN           : num [1:309] 1 1 1 1 0 0 1 0 0 1 ...
##  $ WEIGHT               : num [1:309] 113 136 153 142 144 ...
##  $ HEIGHT_INCH          : num [1:309] 65.8 71.5 69.4 68.2 67.8 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   LUNG_CANCER = col_double(),
##   ..   GENDER = col_double(),
##   ..   AGE = col_double(),
##   ..   SMOKING = col_double(),
##   ..   YELLOW_FINGERS = col_double(),
##   ..   ANXIETY = col_double(),
##   ..   PEER_PRESSURE = col_double(),
##   ..   CHRONIC_DISEASE = col_double(),
##   ..   FATIGUE = col_double(),
##   ..   ALLERGY = col_double(),
##   ..   WHEEZING = col_double(),
##   ..   ALCOHOL_CONSUMING = col_double(),
##   ..   COUGHING = col_double(),
##   ..   SHORTNESS_OF_BREATH = col_double(),
##   ..   SWALLOWING_DIFFICULTY = col_double(),
##   ..   CHEST_PAIN = col_double(),
##   ..   WEIGHT = col_double(),
##   ..   HEIGHT_INCH = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
attach(cancer)
# Checking if there are null values in the dataset
any(is.na(cancer))
## [1] FALSE
# Splitting data depending on the people diagnosed with lung cancer and Not diagnosed with lung cancer
split_list = split(cancer, f = factor(cancer$LUNG_CANCER))
No_Cancer = split_list[[1]]
Yes_Cancer = split_list[[2]]
# Dropping the first column
NCan = No_Cancer[,-1]
YCan=Yes_Cancer[,-1]
# Calculating the Mean of each column for People diagnosed with and without lung cancer
colMeans(NCan)
##                GENDER                   AGE               SMOKING 
##             0.5641026            60.7435897             0.5128205 
##        YELLOW_FINGERS               ANXIETY         PEER_PRESSURE 
##             0.3333333             0.3076923             0.2564103 
##       CHRONIC_DISEASE               FATIGUE               ALLERGY 
##             0.3589744             0.4871795             0.1282051 
##              WHEEZING     ALCOHOL_CONSUMING              COUGHING 
##             0.2307692             0.1794872             0.2564103 
##   SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY            CHEST_PAIN 
##             0.5641026             0.1282051             0.3076923 
##                WEIGHT           HEIGHT_INCH 
##           126.0224131            67.8409054
colMeans(YCan)
##                GENDER                   AGE               SMOKING 
##             0.4629630            62.9518519             0.4259259 
##        YELLOW_FINGERS               ANXIETY         PEER_PRESSURE 
##             0.6037037             0.5259259             0.5370370 
##       CHRONIC_DISEASE               FATIGUE               ALLERGY 
##             0.5259259             0.7000000             0.6185185 
##              WHEEZING     ALCOHOL_CONSUMING              COUGHING 
##             0.6037037             0.6111111             0.6259259 
##   SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY            CHEST_PAIN 
##             0.6518519             0.5185185             0.5925926 
##                WEIGHT           HEIGHT_INCH 
##           126.8383662            67.9485751
# Calculating the Covariance of each column for People diagnosed with and without lung cancer
NC_cov = cov(NCan, y=NULL, method = "pearson")
NC_cov
##                            GENDER         AGE       SMOKING YELLOW_FINGERS
## GENDER                 0.25236167  0.04318489  0.0188933873  -8.771930e-03
## AGE                    0.04318489 92.72199730  0.4770580297  -1.017544e+00
## SMOKING                0.01889339  0.47705803  0.2564102564   8.771930e-03
## YELLOW_FINGERS        -0.00877193 -1.01754386  0.0087719298   2.280702e-01
## ANXIETY               -0.07287449 -0.20850202  0.0222672065   5.263158e-02
## PEER_PRESSURE         -0.06950067  0.56747638  0.0229419703  -3.508772e-02
## CHRONIC_DISEASE        0.05533063 -0.19500675  0.0479082321  -7.017544e-02
## FATIGUE                0.08636977  0.23346829  0.0067476383  -1.403509e-01
## ALLERGY               -0.02159244 -0.93994602 -0.0674763833  -4.385965e-02
## WHEEZING              -0.02834008  0.37651822  0.0627530364  -6.062973e-21
## ALCOHOL_CONSUMING     -0.10391363  0.38933873  0.0107962213  -8.771930e-03
## COUGHING              -0.01686910  0.48852901  0.0492577598   4.385965e-02
## SHORTNESS_OF_BREATH    0.09446694 -0.06207827  0.0452091768  -6.140351e-02
## SWALLOWING_DIFFICULTY -0.04790823 -0.62415655  0.0114709852   6.140351e-02
## CHEST_PAIN            -0.12550607 -0.34008097 -0.0303643725   2.631579e-02
## WEIGHT                -0.11867047  8.60870607  1.8616220648   8.314850e-01
## HEIGHT_INCH           -0.08300706 -0.56136069 -0.0008346761   2.831242e-01
##                            ANXIETY PEER_PRESSURE CHRONIC_DISEASE      FATIGUE
## GENDER                -0.072874494  -0.069500675     0.055330634  0.086369771
## AGE                   -0.208502024   0.567476383    -0.195006748  0.233468286
## SMOKING                0.022267206   0.022941970     0.047908232  0.006747638
## YELLOW_FINGERS         0.052631579  -0.035087719    -0.070175439 -0.140350877
## ANXIETY                0.218623482  -0.002024291    -0.034412955 -0.074898785
## PEER_PRESSURE         -0.002024291   0.195681511     0.010796221 -0.049257760
## CHRONIC_DISEASE       -0.034412955   0.010796221     0.236167341  0.031039136
## FATIGUE               -0.074898785  -0.049257760     0.031039136  0.256410256
## ALLERGY               -0.040485830  -0.033738192     0.005398111  0.014844804
## WHEEZING              -0.072874494   0.018218623    -0.058704453 -0.010121457
## ALCOHOL_CONSUMING      0.048582996   0.031713900     0.012820513 -0.063427800
## COUGHING              -0.028340081   0.011470985    -0.094466937 -0.049257760
## SHORTNESS_OF_BREATH   -0.151821862  -0.043184885     0.029014845  0.139001350
## SWALLOWING_DIFFICULTY  0.064777328  -0.033738192    -0.020917679 -0.064102564
## CHEST_PAIN            -0.018218623   0.050607287    -0.087044534 -0.048582996
## WEIGHT                -0.377730445   1.331191296     1.293040182 -1.013774696
## HEIGHT_INCH           -0.037506700   0.086397794    -0.052091721 -0.239720061
##                            ALLERGY      WHEEZING ALCOHOL_CONSUMING     COUGHING
## GENDER                -0.021592443 -2.834008e-02      -0.103913630 -0.016869096
## AGE                   -0.939946019  3.765182e-01       0.389338731  0.488529015
## SMOKING               -0.067476383  6.275304e-02       0.010796221  0.049257760
## YELLOW_FINGERS        -0.043859649 -6.062973e-21      -0.008771930  0.043859649
## ANXIETY               -0.040485830 -7.287449e-02       0.048582996 -0.028340081
## PEER_PRESSURE         -0.033738192  1.821862e-02       0.031713900  0.011470985
## CHRONIC_DISEASE        0.005398111 -5.870445e-02       0.012820513 -0.094466937
## FATIGUE                0.014844804 -1.012146e-02      -0.063427800 -0.049257760
## ALLERGY                0.114709852  2.226721e-02       0.029014845  0.018893387
## WHEEZING               0.022267206  1.821862e-01       0.036437247  0.123481781
## ALCOHOL_CONSUMING      0.029014845  3.643725e-02       0.151147099  0.031713900
## COUGHING               0.018893387  1.234818e-01       0.031713900  0.195681511
## SHORTNESS_OF_BREATH    0.004723347  5.060729e-02      -0.077597841  0.009446694
## SWALLOWING_DIFFICULTY -0.016869096 -4.048583e-03       0.002699055 -0.033738192
## CHEST_PAIN             0.038461538  5.870445e-02       0.022267206  0.024291498
## WEIGHT                -1.441954089 -7.620952e-01      -0.742439251  0.361533401
## HEIGHT_INCH           -0.063099656 -5.507328e-03      -0.131474413  0.003802530
##                       SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY  CHEST_PAIN
## GENDER                        0.094466937          -0.047908232 -0.12550607
## AGE                          -0.062078273          -0.624156545 -0.34008097
## SMOKING                       0.045209177           0.011470985 -0.03036437
## YELLOW_FINGERS               -0.061403509           0.061403509  0.02631579
## ANXIETY                      -0.151821862           0.064777328 -0.01821862
## PEER_PRESSURE                -0.043184885          -0.033738192  0.05060729
## CHRONIC_DISEASE               0.029014845          -0.020917679 -0.08704453
## FATIGUE                       0.139001350          -0.064102564 -0.04858300
## ALLERGY                       0.004723347          -0.016869096  0.03846154
## WHEEZING                      0.050607287          -0.004048583  0.05870445
## ALCOHOL_CONSUMING            -0.077597841           0.002699055  0.02226721
## COUGHING                      0.009446694          -0.033738192  0.02429150
## SHORTNESS_OF_BREATH           0.252361673          -0.021592443 -0.07287449
## SWALLOWING_DIFFICULTY        -0.021592443           0.114709852  0.03846154
## CHEST_PAIN                   -0.072874494           0.038461538  0.21862348
## WEIGHT                        0.234321640           0.642771964  1.25047219
## HEIGHT_INCH                  -0.119816802           0.101810607  0.29252462
##                            WEIGHT   HEIGHT_INCH
## GENDER                 -0.1186705 -0.0830070648
## AGE                     8.6087061 -0.5613606883
## SMOKING                 1.8616221 -0.0008346761
## YELLOW_FINGERS          0.8314850  0.2831242105
## ANXIETY                -0.3777304 -0.0375067004
## PEER_PRESSURE           1.3311913  0.0863977935
## CHRONIC_DISEASE         1.2930402 -0.0520917206
## FATIGUE                -1.0137747 -0.2397200607
## ALLERGY                -1.4419541 -0.0630996559
## WHEEZING               -0.7620952 -0.0055073279
## ALCOHOL_CONSUMING      -0.7424393 -0.1314744130
## COUGHING                0.3615334  0.0038025304
## SHORTNESS_OF_BREATH     0.2343216 -0.1198168016
## SWALLOWING_DIFFICULTY   0.6427720  0.1018106073
## CHEST_PAIN              1.2504722  0.2925246154
## WEIGHT                241.1258039 14.4006850789
## HEIGHT_INCH            14.4006851  3.9074716169
YC_cov = cov(YCan, y=NULL, method = "pearson")
YC_cov
##                             GENDER         AGE      SMOKING YELLOW_FINGERS
## GENDER                 0.249552527 -0.07799807  0.006539997    0.065193446
## AGE                   -0.077998072 63.46607462  0.351438799    0.092372298
## SMOKING                0.006539997  0.35143880  0.245422002    0.005851576
## YELLOW_FINGERS         0.065193446  0.09237230  0.005851576    0.240134930
## ANXIETY                0.056725871  0.21872504 -0.046399559    0.146000275
## PEER_PRESSURE          0.092454908 -0.07070081  0.012047363    0.087222911
## CHRONIC_DISEASE        0.053008399 -0.07867272  0.035384827    0.015888751
## FATIGUE                0.013011152 -0.03680297  0.009293680   -0.018959108
## ALLERGY               -0.034627564  0.12654550  0.014387994   -0.051369957
## WHEEZING              -0.031460829  0.09980724  0.031873881   -0.034958006
## ALCOHOL_CONSUMING     -0.109252375  0.10016522  0.017554729   -0.095208591
## COUGHING              -0.030634724  0.61760980  0.033526091   -0.022401212
## SHORTNESS_OF_BREATH    0.005645050 -0.09489192 -0.022167149   -0.023241085
## SWALLOWING_DIFFICULTY  0.034145670 -0.02698609 -0.006058103    0.076139336
## CHEST_PAIN            -0.082059755 -0.11634311 -0.026573041   -0.043095140
## WEIGHT                -0.047533189 -4.65109152  0.803828195   -0.140955443
## HEIGHT_INCH            0.077151769 -1.12060563  0.086951251    0.072994955
##                            ANXIETY PEER_PRESSURE CHRONIC_DISEASE      FATIGUE
## GENDER                 0.056725871   0.092454908     0.053008399  0.013011152
## AGE                    0.218725045  -0.070700812    -0.078672725 -0.036802974
## SMOKING               -0.046399559   0.012047363     0.035384827  0.009293680
## YELLOW_FINGERS         0.146000275   0.087222911     0.015888751 -0.018959108
## ANXIETY                0.250254716   0.054798293    -0.002533388 -0.046096654
## PEER_PRESSURE          0.054798293   0.249552527     0.006471155  0.020446097
## CHRONIC_DISEASE       -0.002533388   0.006471155     0.250254716 -0.038661710
## FATIGUE               -0.046096654   0.020446097    -0.038661710  0.210780669
## ALLERGY               -0.055128735  -0.036004406     0.019220708 -0.014498141
## WHEEZING              -0.054743219  -0.035453669    -0.013851026  0.029368030
## ALCOHOL_CONSUMING     -0.066088393  -0.065468815    -0.010326311 -0.053903346
## COUGHING              -0.070191381  -0.039997246    -0.044169076  0.036059480
## SHORTNESS_OF_BREATH   -0.020680160  -0.057689660    -0.013245215  0.092193309
## SWALLOWING_DIFFICULTY  0.120335949   0.095965854     0.016246730 -0.037174721
## CHEST_PAIN            -0.037725458  -0.044334297    -0.004268209 -0.003717472
## WEIGHT                -0.312690050   0.264830587     0.215515340  0.078117227
## HEIGHT_INCH            0.025450407   0.062675778     0.050430370  0.089662011
##                           ALLERGY      WHEEZING ALCOHOL_CONSUMING     COUGHING
## GENDER                -0.03462756 -0.0314608289      -0.109252375 -0.030634724
## AGE                    0.12654550  0.0998072422       0.100165221  0.617609803
## SMOKING                0.01438799  0.0318738813       0.017554729  0.033526091
## YELLOW_FINGERS        -0.05136996 -0.0349580063      -0.095208591 -0.022401212
## ANXIETY               -0.05512873 -0.0547432191      -0.066088393 -0.070191381
## PEER_PRESSURE         -0.03600441 -0.0354536693      -0.065468815 -0.039997246
## CHRONIC_DISEASE        0.01922071 -0.0138510257      -0.010326311 -0.044169076
## FATIGUE               -0.01449814  0.0293680297      -0.053903346  0.036059480
## ALLERGY                0.23683051  0.0229794851       0.066707972  0.027770894
## WHEEZING               0.02297949  0.2401349305       0.049772821  0.070535591
## ALCOHOL_CONSUMING      0.06670797  0.0497728211       0.238537794  0.032424618
## COUGHING               0.02777089  0.0705355914       0.032424618  0.235013080
## SHORTNESS_OF_BREATH   -0.01434669 -0.0009362522      -0.042957456  0.070026160
## SWALLOWING_DIFFICULTY -0.03937767  0.0017898940      -0.024370095 -0.058102712
## CHEST_PAIN             0.04474735  0.0201018863       0.075175547  0.006884208
## WEIGHT                 0.68835610  0.3666331070      -0.071185861 -0.137099969
## HEIGHT_INCH            0.06298473  0.0115764421      -0.004233707 -0.028255232
##                       SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY    CHEST_PAIN
## GENDER                       0.0056450503          0.0341456698 -0.0820597549
## AGE                         -0.0948919179         -0.0269860939 -0.1163431089
## SMOKING                     -0.0221671486         -0.0060581027 -0.0265730414
## YELLOW_FINGERS              -0.0232410850          0.0761393364 -0.0430951397
## ANXIETY                     -0.0206801597          0.1203359493 -0.0377254578
## PEER_PRESSURE               -0.0576896599          0.0959658543 -0.0443342971
## CHRONIC_DISEASE             -0.0132452155          0.0162467300 -0.0042682087
## FATIGUE                      0.0921933086         -0.0371747212 -0.0037174721
## ALLERGY                     -0.0143466887         -0.0393776676  0.0447473496
## WHEEZING                    -0.0009362522          0.0017898940  0.0201018863
## ALCOHOL_CONSUMING           -0.0429574556         -0.0243700950  0.0751755473
## COUGHING                     0.0700261600         -0.0581027124  0.0068842076
## SHORTNESS_OF_BREATH          0.2277846620         -0.0455734545  0.0137684153
## SWALLOWING_DIFFICULTY       -0.0455734545          0.2505851576  0.0001376842
## CHEST_PAIN                   0.0137684153          0.0001376842  0.2423241085
## WEIGHT                       0.0346854829          0.2201749401  0.2258873028
## HEIGHT_INCH                 -0.0338105689          0.0828150916  0.0639443426
##                             WEIGHT  HEIGHT_INCH
## GENDER                 -0.04753319  0.077151769
## AGE                    -4.65109152 -1.120605628
## SMOKING                 0.80382819  0.086951251
## YELLOW_FINGERS         -0.14095544  0.072994955
## ANXIETY                -0.31269005  0.025450407
## PEER_PRESSURE           0.26483059  0.062675778
## CHRONIC_DISEASE         0.21551534  0.050430370
## FATIGUE                 0.07811723  0.089662011
## ALLERGY                 0.68835610  0.062984731
## WHEEZING                0.36663311  0.011576442
## ALCOHOL_CONSUMING      -0.07118586 -0.004233707
## COUGHING               -0.13709997 -0.028255232
## SHORTNESS_OF_BREATH     0.03468548 -0.033810569
## SWALLOWING_DIFFICULTY   0.22017494  0.082815092
## CHEST_PAIN              0.22588730  0.063944343
## WEIGHT                132.52068523 11.065946698
## HEIGHT_INCH            11.06594670  3.699899104
# Calculating the Correlation of each column for People diagnosed with and without lung cancer
NC_corr = cor(NCan, y=NULL,  method = "pearson")
NC_corr
##                             GENDER          AGE       SMOKING YELLOW_FINGERS
## GENDER                 1.000000000  0.008927476  0.0742729086  -3.656362e-02
## AGE                    0.008927476  1.000000000  0.0978390269  -2.212725e-01
## SMOKING                0.074272909  0.097839027  1.0000000000   3.627381e-02
## YELLOW_FINGERS        -0.036563621 -0.221272529  0.0362738125   1.000000e+00
## ANXIETY               -0.310252614 -0.046309542  0.0940480156   2.357023e-01
## PEER_PRESSURE         -0.312753677  0.133223705  0.1024207896  -1.660910e-01
## CHRONIC_DISEASE        0.226643897 -0.041672382  0.1946850165  -3.023716e-01
## FATIGUE                0.339533297  0.047881617  0.0263157895  -5.803810e-01
## ALLERGY               -0.126908209 -0.288211407 -0.3934447377  -2.711631e-01
## WHEEZING              -0.132169610  0.091608722  0.2903416016  -2.974360e-20
## ALCOHOL_CONSUMING     -0.532060368  0.104000712  0.0548408497  -4.724556e-02
## COUGHING              -0.075911087  0.114689610  0.2199034601   2.076137e-01
## SHORTNESS_OF_BREATH    0.374331551 -0.012833246  0.1777244600  -2.559453e-01
## SWALLOWING_DIFFICULTY -0.281577590 -0.191382305  0.0668856054   3.796283e-01
## CHEST_PAIN            -0.534323946 -0.075534010 -0.1282472940   1.178511e-01
## WEIGHT                -0.015212798  0.057573767  0.2367565359   1.121239e-01
## HEIGHT_INCH           -0.083590215 -0.029491896 -0.0008338777   2.999127e-01
##                            ANXIETY PEER_PRESSURE CHRONIC_DISEASE     FATIGUE
## GENDER                -0.310252614  -0.312753677      0.22664390  0.33953330
## AGE                   -0.046309542   0.133223705     -0.04167238  0.04788162
## SMOKING                0.094048016   0.102420790      0.19468502  0.02631579
## YELLOW_FINGERS         0.235702260  -0.166090960     -0.30237158 -0.58038100
## ANXIETY                1.000000000  -0.009787004     -0.15144804 -0.31634333
## PEER_PRESSURE         -0.009787004   1.000000000      0.05022119 -0.21990346
## CHRONIC_DISEASE       -0.151448037   0.050221186      1.00000000  0.12613395
## FATIGUE               -0.316343325  -0.219903460      0.12613395  1.00000000
## ALLERGY               -0.255654996  -0.225188675      0.03279680  0.08655784
## WHEEZING              -0.365148372   0.096490128     -0.28301102 -0.04682929
## ALCOHOL_CONSUMING      0.267261242   0.184405916      0.06785714 -0.32218999
## COUGHING              -0.137018051   0.058620690     -0.43943537 -0.21990346
## SHORTNESS_OF_BREATH   -0.646359612  -0.194332382      0.11884985  0.54643640
## SWALLOWING_DIFFICULTY  0.409047994  -0.225188675     -0.12708761 -0.37377250
## CHEST_PAIN            -0.083333333   0.244675091     -0.38307445 -0.20519567
## WEIGHT                -0.052024959   0.193795518      0.17134848 -0.12892938
## HEIGHT_INCH           -0.040580046   0.098805208     -0.05422641 -0.23949076
##                           ALLERGY      WHEEZING ALCOHOL_CONSUMING     COUGHING
## GENDER                -0.12690821 -1.321696e-01       -0.53206037 -0.075911087
## AGE                   -0.28821141  9.160872e-02        0.10400071  0.114689610
## SMOKING               -0.39344474  2.903416e-01        0.05484085  0.219903460
## YELLOW_FINGERS        -0.27116307 -2.974360e-20       -0.04724556  0.207613700
## ANXIETY               -0.25565500 -3.651484e-01        0.26726124 -0.137018051
## PEER_PRESSURE         -0.22518867  9.649013e-02        0.18440592  0.058620690
## CHRONIC_DISEASE        0.03279680 -2.830110e-01        0.06785714 -0.439435374
## FATIGUE                0.08655784 -4.682929e-02       -0.32218999 -0.219903460
## ALLERGY                1.00000000  1.540308e-01        0.22035352  0.126105658
## WHEEZING               0.15403081  1.000000e+00        0.21957752  0.653988646
## ALCOHOL_CONSUMING      0.22035352  2.195775e-01        1.00000000  0.184405916
## COUGHING               0.12610566  6.539886e-01        0.18440592  1.000000000
## SHORTNESS_OF_BREATH    0.02776117  2.360172e-01       -0.39731781  0.042510209
## SWALLOWING_DIFFICULTY -0.14705882 -2.800560e-02        0.02049800 -0.225188675
## CHEST_PAIN             0.24287225  2.941473e-01        0.12249474  0.117444044
## WEIGHT                -0.27417587 -1.149819e-01       -0.12298133  0.052632220
## HEIGHT_INCH           -0.09424943 -6.527325e-03       -0.17107771  0.004348604
##                       SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY  CHEST_PAIN
## GENDER                         0.37433155           -0.28157759 -0.53432395
## AGE                           -0.01283325           -0.19138231 -0.07553401
## SMOKING                        0.17772446            0.06688561 -0.12824729
## YELLOW_FINGERS                -0.25594535            0.37962830  0.11785113
## ANXIETY                       -0.64635961            0.40904799 -0.08333333
## PEER_PRESSURE                 -0.19433238           -0.22518867  0.24467509
## CHRONIC_DISEASE                0.11884985           -0.12708761 -0.38307445
## FATIGUE                        0.54643640           -0.37377250 -0.20519567
## ALLERGY                        0.02776117           -0.14705882  0.24287225
## WHEEZING                       0.23601716           -0.02800560  0.29414730
## ALCOHOL_CONSUMING             -0.39731781            0.02049800  0.12249474
## COUGHING                       0.04251021           -0.22518867  0.11744404
## SHORTNESS_OF_BREATH            1.00000000           -0.12690821 -0.31025261
## SWALLOWING_DIFFICULTY         -0.12690821            1.00000000  0.24287225
## CHEST_PAIN                    -0.31025261            0.24287225  1.00000000
## WEIGHT                         0.03003854            0.12221787  0.17222801
## HEIGHT_INCH                   -0.12065855            0.15207042  0.31649445
##                            WEIGHT   HEIGHT_INCH
## GENDER                -0.01521280 -0.0835902149
## AGE                    0.05757377 -0.0294918958
## SMOKING                0.23675654 -0.0008338777
## YELLOW_FINGERS         0.11212393  0.2999126913
## ANXIETY               -0.05202496 -0.0405800465
## PEER_PRESSURE          0.19379552  0.0988052083
## CHRONIC_DISEASE        0.17134848 -0.0542264116
## FATIGUE               -0.12892938 -0.2394907624
## ALLERGY               -0.27417587 -0.0942494264
## WHEEZING              -0.11498193 -0.0065273251
## ALCOHOL_CONSUMING     -0.12298133 -0.1710777055
## COUGHING               0.05263222  0.0043486042
## SHORTNESS_OF_BREATH    0.03003854 -0.1206585514
## SWALLOWING_DIFFICULTY  0.12221787  0.1520704227
## CHEST_PAIN             0.17222801  0.3164944493
## WEIGHT                 1.00000000  0.4691518064
## HEIGHT_INCH            0.46915181  1.0000000000
YC_corr = cor(YCan, y=NULL,  method = "pearson")
YC_corr
##                             GENDER          AGE     SMOKING YELLOW_FINGERS
## GENDER                 1.000000000 -0.019598917  0.02642651     0.26631479
## AGE                   -0.019598917  1.000000000  0.08904758     0.02366155
## SMOKING                0.026426511  0.089047584  1.00000000     0.02410396
## YELLOW_FINGERS         0.266314789  0.023661554  0.02410396     1.00000000
## ANXIETY                0.226991216  0.054882838 -0.18722592     0.59557282
## PEER_PRESSURE          0.370482759 -0.017765302  0.04868042     0.35630500
## CHRONIC_DISEASE        0.212115578 -0.019740686  0.14278060     0.06481432
## FATIGUE                0.056730863 -0.010062287  0.04086162    -0.08427036
## ALLERGY               -0.142436776  0.032640521  0.05967943    -0.21540844
## WHEEZING              -0.128517274  0.025566046  0.13129571    -0.14557652
## ALCOHOL_CONSUMING     -0.447786815  0.025743497  0.07255357    -0.39780467
## COUGHING              -0.126498964  0.159917998  0.13959831    -0.09429699
## SHORTNESS_OF_BREATH    0.023676886 -0.024957218 -0.09375422    -0.09937256
## SWALLOWING_DIFFICULTY  0.136545370 -0.006766928 -0.02442880     0.31038716
## CHEST_PAIN            -0.333695937 -0.029666857 -0.10896479    -0.17864971
## WEIGHT                -0.008265595 -0.050715677  0.14094986    -0.02498690
## HEIGHT_INCH            0.080291572 -0.073128563  0.09124817     0.07744087
##                           ANXIETY PEER_PRESSURE CHRONIC_DISEASE     FATIGUE
## GENDER                 0.22699122    0.37048276      0.21211558  0.05673086
## AGE                    0.05488284   -0.01776530     -0.01974069 -0.01006229
## SMOKING               -0.18722592    0.04868042      0.14278060  0.04086162
## YELLOW_FINGERS         0.59557282    0.35630500      0.06481432 -0.08427036
## ANXIETY                1.00000000    0.21927792     -0.01012324 -0.20070717
## PEER_PRESSURE          0.21927792    1.00000000      0.02589463  0.08914850
## CHRONIC_DISEASE       -0.01012324    0.02589463      1.00000000 -0.16833504
## FATIGUE               -0.20070717    0.08914850     -0.16833504  1.00000000
## ALLERGY               -0.22644778   -0.14810027      0.07895132 -0.06489005
## WHEEZING              -0.22331173   -0.14482800     -0.05650191  0.13053644
## ALCOHOL_CONSUMING     -0.27049264   -0.26833350     -0.04226448 -0.24039295
## COUGHING              -0.28943206   -0.16515932     -0.18212986  0.16201605
## SHORTNESS_OF_BREATH   -0.08661648   -0.24196623     -0.05547607  0.42074772
## SWALLOWING_DIFFICULTY  0.48053672    0.38375856      0.06487796 -0.16175386
## CHEST_PAIN            -0.15319517   -0.18028539     -0.01733230 -0.01644879
## WEIGHT                -0.05429766    0.04605166      0.03742357  0.01478052
## HEIGHT_INCH            0.02644896    0.06522646      0.05240902  0.10153088
##                           ALLERGY     WHEEZING ALCOHOL_CONSUMING    COUGHING
## GENDER                -0.14243678 -0.128517274      -0.447786815 -0.12649896
## AGE                    0.03264052  0.025566046       0.025743497  0.15991800
## SMOKING                0.05967943  0.131295710       0.072553571  0.13959831
## YELLOW_FINGERS        -0.21540844 -0.145576515      -0.397804665 -0.09429699
## ANXIETY               -0.22644778 -0.223311726      -0.270492644 -0.28943206
## PEER_PRESSURE         -0.14810027 -0.144828000      -0.268333498 -0.16515932
## CHRONIC_DISEASE        0.07895132 -0.056501910      -0.042264476 -0.18212986
## FATIGUE               -0.06489005  0.130536437      -0.240392953  0.16201605
## ALLERGY                1.00000000  0.096359336       0.280659865  0.11771316
## WHEEZING               0.09635934  1.000000000       0.207962959  0.29691670
## ALCOHOL_CONSUMING      0.28065986  0.207962959       1.000000000  0.13694628
## COUGHING               0.11771316  0.296916700       0.136946283  1.00000000
## SHORTNESS_OF_BREATH   -0.06176901 -0.004003160      -0.184288278  0.30265793
## SWALLOWING_DIFFICULTY -0.16164173  0.007296624      -0.099678375 -0.23942678
## CHEST_PAIN             0.18678852  0.083331813       0.312679700  0.02884760
## WEIGHT                 0.12287188  0.064992340      -0.012661154 -0.02456685
## HEIGHT_INCH            0.06728550  0.012281531      -0.004506582 -0.03030107
##                       SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY    CHEST_PAIN
## GENDER                        0.023676886          0.1365453702 -0.3336959365
## AGE                          -0.024957218         -0.0067669277 -0.0296668567
## SMOKING                      -0.093754225         -0.0244288045 -0.1089647949
## YELLOW_FINGERS               -0.099372563          0.3103871593 -0.1786497088
## ANXIETY                      -0.086616477          0.4805367221 -0.1531951696
## PEER_PRESSURE                -0.241966228          0.3837585606 -0.1802853885
## CHRONIC_DISEASE              -0.055476066          0.0648779556 -0.0173323002
## FATIGUE                       0.420747721         -0.1617538620 -0.0164487924
## ALLERGY                      -0.061769006         -0.1616417305  0.1867885192
## WHEEZING                     -0.004003160          0.0072966240  0.0833318130
## ALCOHOL_CONSUMING            -0.184288278         -0.0996783753  0.3126797004
## COUGHING                      0.302657929         -0.2394267761  0.0288475963
## SHORTNESS_OF_BREATH           1.000000000         -0.1907532908  0.0586034799
## SWALLOWING_DIFFICULTY        -0.190753291          1.0000000000  0.0005587377
## CHEST_PAIN                    0.058603480          0.0005587377  1.0000000000
## WEIGHT                        0.006313115          0.0382074786  0.0398613196
## HEIGHT_INCH                  -0.036829456          0.0860076089  0.0675318853
##                             WEIGHT  HEIGHT_INCH
## GENDER                -0.008265595  0.080291572
## AGE                   -0.050715677 -0.073128563
## SMOKING                0.140949861  0.091248166
## YELLOW_FINGERS        -0.024986898  0.077440872
## ANXIETY               -0.054297657  0.026448963
## PEER_PRESSURE          0.046051663  0.065226460
## CHRONIC_DISEASE        0.037423570  0.052409025
## FATIGUE                0.014780516  0.101530879
## ALLERGY                0.122871880  0.067285504
## WHEEZING               0.064992340  0.012281531
## ALCOHOL_CONSUMING     -0.012661154 -0.004506582
## COUGHING              -0.024566852 -0.030301067
## SHORTNESS_OF_BREATH    0.006313115 -0.036829456
## SWALLOWING_DIFFICULTY  0.038207479  0.086007609
## CHEST_PAIN             0.039861320  0.067531885
## WEIGHT                 1.000000000  0.499748843
## HEIGHT_INCH            0.499748843  1.000000000
# Plotting a matrix for Correlation for People diagnosed with and without lung cancer
library(ggcorrplot)
## Loading required package: ggplot2
ggcorrplot(NC_corr, lab = TRUE)

ggcorrplot(YC_corr, lab = TRUE)

#Boxplot
ggplot(cancer,aes(y=AGE, fill=LUNG_CANCER))+geom_boxplot()+ labs(title='Comparison between age of people')
## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

#Load packages
library(lattice)
library(ggplot2)
library(ggridges)
library(ggvis)
## 
## Attaching package: 'ggvis'
## 
## The following object is masked from 'package:ggplot2':
## 
##     resolution
library(ggthemes)
library(cowplot)
## 
## Attaching package: 'cowplot'
## 
## The following object is masked from 'package:ggthemes':
## 
##     theme_map
library(gapminder)
library(gganimate)
## No renderer backend detected. gganimate will default to writing frames to separate files
## Consider installing:
## - the `gifski` package for gif output
## - the `av` package for video output
## and restarting the R session
## 
## Attaching package: 'gganimate'
## 
## The following object is masked from 'package:ggvis':
## 
##     view_static
library(dplyr)
## 
## Attaching package: 'dplyr'
## 
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## 
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ tibble  3.2.1     ✔ stringr 1.5.0
## ✔ tidyr   1.3.0     ✔ forcats 1.0.0
## ✔ purrr   1.0.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter()     masks stats::filter()
## ✖ dplyr::lag()        masks stats::lag()
## ✖ ggvis::resolution() masks ggplot2::resolution()
library(grid)
library(gridExtra)
## 
## Attaching package: 'gridExtra'
## 
## The following object is masked from 'package:dplyr':
## 
##     combine
library(RColorBrewer)
# GGplot
ggplot(cancer, aes(x=WEIGHT,y=AGE)) + geom_point()

ggplot(cancer, aes(x=WEIGHT,y=HEIGHT_INCH)) + facet_wrap(~LUNG_CANCER) + geom_point()

ggplot(cancer, aes(x=HEIGHT_INCH, y=AGE)) +geom_point(aes(color=PEER_PRESSURE))

ggplot(cancer, aes(x=HEIGHT_INCH,y=AGE)) + xlim(50,80) + geom_point(colour="steelblue", pch=3) + 
  labs(x="HEIGHT IN INCHES", y="AGE", title="LUNG CANCER Data") 

#Histogram
ggplot(cancer, aes(AGE))+geom_histogram(bins=10)

ggplot(cancer, aes(AGE))+geom_histogram(aes(fill = after_stat(count)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

#Regression
ggplot(cancer, aes(x=WEIGHT, y=AGE)) + geom_point() + geom_smooth(method=lm)
## `geom_smooth()` using formula = 'y ~ x'

ggplot(cancer, aes(x=HEIGHT_INCH, y=AGE)) + geom_point() + stat_smooth()
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

#Violin Plot
ggplot(cancer, aes(x=LUNG_CANCER, y=AGE)) + geom_violin()

ggplot(cancer, aes(x=LUNG_CANCER, y=WEIGHT)) + geom_violin()

ggplot(cancer, aes(x=LUNG_CANCER, y=HEIGHT_INCH)) + geom_violin()

#Boxplot
ggplot(cancer, aes(x=LUNG_CANCER, y=WEIGHT)) + geom_boxplot()
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?

ggplot(cancer, aes(x=LUNG_CANCER, y=WEIGHT)) + geom_boxplot() + coord_flip()
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?

#Density Plot and ggridges
ggplot(cancer, aes(x=AGE)) + geom_density() 

ggplot(cancer, aes(x=AGE, fill=LUNG_CANCER, color=LUNG_CANCER)) + geom_density() 
## Warning: The following aesthetics were dropped during statistical transformation: fill,
## colour
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

ggplot(cancer, aes(x=AGE, fill=LUNG_CANCER, color=LUNG_CANCER)) + geom_density(alpha=0.3, aes(y=..scaled..)) 
## Warning: The dot-dot notation (`..scaled..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(scaled)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## Warning: The following aesthetics were dropped during statistical transformation: fill,
## colour
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

#Hexbin
ggplot(cancer, aes(x=HEIGHT_INCH, y=AGE)) + geom_hex()

PCA

library(readr)
cancer <- read_csv("/Users/batul/Desktop/MVA/LUNGCANCER3.csv")
## Rows: 309 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (18): LUNG_CANCER, GENDER, AGE, SMOKING, YELLOW_FINGERS, ANXIETY, PEER_P...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
str(cancer)
## spc_tbl_ [309 × 18] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ LUNG_CANCER          : num [1:309] 1 1 0 0 0 1 1 1 0 1 ...
##  $ GENDER               : num [1:309] 0 0 1 0 1 1 0 1 1 0 ...
##  $ AGE                  : num [1:309] 69 74 59 63 63 75 52 51 68 53 ...
##  $ SMOKING              : num [1:309] 1 0 1 0 1 1 0 0 0 0 ...
##  $ YELLOW_FINGERS       : num [1:309] 1 0 0 1 1 1 0 1 0 1 ...
##  $ ANXIETY              : num [1:309] 1 0 0 1 0 0 0 1 1 1 ...
##  $ PEER_PRESSURE        : num [1:309] 0 0 1 0 0 0 0 1 0 1 ...
##  $ CHRONIC_DISEASE      : num [1:309] 0 1 0 0 0 1 0 0 0 1 ...
##  $ FATIGUE              : num [1:309] 1 1 1 0 0 1 1 1 1 0 ...
##  $ ALLERGY              : num [1:309] 0 1 0 0 0 1 0 1 0 1 ...
##  $ WHEEZING             : num [1:309] 1 0 1 0 1 1 1 0 0 0 ...
##  $ ALCOHOL_CONSUMING    : num [1:309] 1 0 0 1 0 0 1 0 0 1 ...
##  $ COUGHING             : num [1:309] 1 0 1 0 1 1 1 0 0 0 ...
##  $ SHORTNESS_OF_BREATH  : num [1:309] 1 1 1 0 1 1 1 1 0 0 ...
##  $ SWALLOWING_DIFFICULTY: num [1:309] 1 1 0 1 0 0 0 1 0 1 ...
##  $ CHEST_PAIN           : num [1:309] 1 1 1 1 0 0 1 0 0 1 ...
##  $ WEIGHT               : num [1:309] 113 136 153 142 144 ...
##  $ HEIGHT_INCH          : num [1:309] 65.8 71.5 69.4 68.2 67.8 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   LUNG_CANCER = col_double(),
##   ..   GENDER = col_double(),
##   ..   AGE = col_double(),
##   ..   SMOKING = col_double(),
##   ..   YELLOW_FINGERS = col_double(),
##   ..   ANXIETY = col_double(),
##   ..   PEER_PRESSURE = col_double(),
##   ..   CHRONIC_DISEASE = col_double(),
##   ..   FATIGUE = col_double(),
##   ..   ALLERGY = col_double(),
##   ..   WHEEZING = col_double(),
##   ..   ALCOHOL_CONSUMING = col_double(),
##   ..   COUGHING = col_double(),
##   ..   SHORTNESS_OF_BREATH = col_double(),
##   ..   SWALLOWING_DIFFICULTY = col_double(),
##   ..   CHEST_PAIN = col_double(),
##   ..   WEIGHT = col_double(),
##   ..   HEIGHT_INCH = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
attach(cancer)
## The following objects are masked from cancer (pos = 22):
## 
##     AGE, ALCOHOL_CONSUMING, ALLERGY, ANXIETY, CHEST_PAIN,
##     CHRONIC_DISEASE, COUGHING, FATIGUE, GENDER, HEIGHT_INCH,
##     LUNG_CANCER, PEER_PRESSURE, SHORTNESS_OF_BREATH, SMOKING,
##     SWALLOWING_DIFFICULTY, WEIGHT, WHEEZING, YELLOW_FINGERS
#Load packages
library(lattice)
library(ggplot2)
library(ggridges)
library(ggvis)
library(ggthemes)
library(cowplot)
library(gapminder)
library(gganimate)
library(dplyr)
library(tidyverse)
library(grid)
library(gridExtra)
library(RColorBrewer)

# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
cancer_pca <- prcomp(cancer[,-1],scale=TRUE)
cancer_pca
## Standard deviations (1, .., p=17):
##  [1] 1.6925050 1.3991347 1.2994647 1.2134854 1.1417493 1.0353277 0.9769035
##  [8] 0.9440119 0.9031531 0.8452754 0.7957706 0.7654147 0.7285322 0.7184765
## [15] 0.6352291 0.5647943 0.5262480
## 
## Rotation (n x k) = (17 x 17):
##                                 PC1          PC2         PC3         PC4
## GENDER                 0.3210475112 -0.286879473  0.17379787 -0.07237418
## AGE                   -0.0364649541  0.030795541  0.04688999  0.27943243
## SMOKING               -0.0430283442  0.003424731  0.31567559 -0.10751874
## YELLOW_FINGERS         0.3814759828  0.128104954  0.13853036  0.29389320
## ANXIETY                0.4033326977  0.205543431 -0.07469222  0.26312783
## PEER_PRESSURE          0.3069045925  0.105788877  0.22315119  0.15097246
## CHRONIC_DISEASE        0.0902654180  0.066353796  0.10570086 -0.32228900
## FATIGUE               -0.1024499601 -0.391147209  0.29985430  0.20127738
## ALLERGY               -0.2493507498  0.239694551  0.12271547 -0.02157728
## WHEEZING              -0.2442608884  0.124539773  0.26727611  0.32565680
## ALCOHOL_CONSUMING     -0.3321543572  0.413483478 -0.08463899  0.03187039
## COUGHING              -0.2792205789 -0.058744485  0.24960914  0.42897511
## SHORTNESS_OF_BREATH   -0.1417347885 -0.424686551  0.17846341  0.18710306
## SWALLOWING_DIFFICULTY  0.2925413504  0.343624495  0.11855529  0.25354529
## CHEST_PAIN            -0.2335726303  0.316920719  0.02654379  0.06741104
## WEIGHT                -0.0003161562  0.138055198  0.49723646 -0.33025021
## HEIGHT_INCH            0.0485449546  0.155477544  0.49241846 -0.27906767
##                               PC5         PC6         PC7         PC8
## GENDER                 0.20073240 -0.24182352  0.01184223 -0.03985594
## AGE                    0.33787243  0.23970537  0.59890223 -0.53931034
## SMOKING                0.52742230  0.22454151 -0.15463295  0.20038365
## YELLOW_FINGERS        -0.02429773  0.03987572  0.14776817  0.31135018
## ANXIETY               -0.14203498  0.02100195  0.25209607  0.16394901
## PEER_PRESSURE          0.09868719 -0.13237811 -0.39679983 -0.48888049
## CHRONIC_DISEASE        0.34336849 -0.58708763  0.27268807  0.16305791
## FATIGUE               -0.19343265 -0.19872006 -0.17492007 -0.30793949
## ALLERGY                0.06195362 -0.42347967  0.18154792 -0.13304550
## WHEEZING               0.15239622 -0.07376779 -0.30344915  0.23592177
## ALCOHOL_CONSUMING      0.10964754 -0.04578332 -0.04969458 -0.01545999
## COUGHING               0.13819136  0.11156157  0.09656026  0.21956243
## SHORTNESS_OF_BREATH   -0.26321037 -0.22493715  0.29003504  0.21690138
## SWALLOWING_DIFFICULTY -0.08485041 -0.18711304 -0.12109907  0.02088317
## CHEST_PAIN            -0.36362550 -0.22121918  0.06275957 -0.11472139
## WEIGHT                -0.18496760  0.24504959  0.13211070 -0.01887354
## HEIGHT_INCH           -0.28364547  0.18977120  0.11161979 -0.01894483
##                                PC9         PC10        PC11        PC12
## GENDER                 0.281223963 -0.244510475 -0.19864542  0.05106762
## AGE                   -0.181259271 -0.179178546 -0.05135663  0.09966744
## SMOKING               -0.339753798  0.456246291  0.21657468  0.12513209
## YELLOW_FINGERS         0.158443155  0.321656428 -0.15293052  0.26549819
## ANXIETY               -0.025925593 -0.006524112  0.32378188  0.05972929
## PEER_PRESSURE          0.096840684  0.223908923 -0.20262510 -0.31742172
## CHRONIC_DISEASE       -0.258475999 -0.054485578 -0.19258350 -0.03483907
## FATIGUE               -0.196587965  0.100942472  0.31336340  0.29668046
## ALLERGY                0.539524367  0.193301357  0.42374977  0.12050452
## WHEEZING              -0.038620686 -0.568302398 -0.07283366  0.28908157
## ALCOHOL_CONSUMING     -0.031951385 -0.019777592  0.14861759 -0.21687274
## COUGHING               0.309583479  0.133044654 -0.28342941 -0.32037459
## SHORTNESS_OF_BREATH   -0.217039867  0.069598604  0.09520010 -0.35152144
## SWALLOWING_DIFFICULTY -0.312852651 -0.209578384  0.23533684 -0.25912909
## CHEST_PAIN            -0.292637073  0.281207000 -0.49725726  0.21746471
## WEIGHT                 0.003135894 -0.124979041  0.06520556 -0.37197858
## HEIGHT_INCH            0.109288894 -0.106118071 -0.05641311  0.28916542
##                              PC13        PC14        PC15        PC16
## GENDER                -0.15894162  0.55185603  0.36640789 -0.08405264
## AGE                   -0.04778967 -0.01222126 -0.04085982  0.10718595
## SMOKING               -0.17075516  0.24864171  0.03445354  0.03818447
## YELLOW_FINGERS         0.04413678 -0.28524951  0.08772850  0.24449863
## ANXIETY                0.07894326  0.02454333  0.36258509 -0.24996070
## PEER_PRESSURE          0.11049565 -0.16437026  0.05166587  0.26450112
## CHRONIC_DISEASE        0.26824464 -0.30220749 -0.07820030 -0.16153534
## FATIGUE                0.23102739 -0.15679639  0.13579435 -0.35854302
## ALLERGY               -0.27698525  0.00347222 -0.14402150  0.09185413
## WHEEZING              -0.15780709 -0.21356468  0.10523380  0.20530205
## ALCOHOL_CONSUMING      0.47755491  0.19969356  0.50074175  0.13770113
## COUGHING               0.17712228  0.07652517 -0.18263798 -0.45814232
## SHORTNESS_OF_BREATH   -0.01819713  0.11879426  0.04977730  0.51704680
## SWALLOWING_DIFFICULTY -0.12461765  0.28371676 -0.44270428 -0.11953032
## CHEST_PAIN            -0.30203928  0.21227649  0.16091658 -0.11875744
## WEIGHT                -0.33879401 -0.31881843  0.29309129 -0.17393309
## HEIGHT_INCH            0.46330708  0.27552099 -0.26518467  0.16642627
##                              PC17
## GENDER                 0.16314656
## AGE                    0.05623413
## SMOKING               -0.12035893
## YELLOW_FINGERS         0.48817125
## ANXIETY               -0.54709508
## PEER_PRESSURE         -0.29176685
## CHRONIC_DISEASE       -0.07288202
## FATIGUE                0.20916257
## ALLERGY               -0.05062214
## WHEEZING              -0.18401827
## ALCOHOL_CONSUMING      0.29244662
## COUGHING              -0.07868837
## SHORTNESS_OF_BREATH   -0.11319831
## SWALLOWING_DIFFICULTY  0.30009780
## CHEST_PAIN            -0.07706518
## WEIGHT                 0.14740550
## HEIGHT_INCH           -0.15886979
summary(cancer_pca)
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     1.6925 1.3991 1.29946 1.21349 1.14175 1.03533 0.97690
## Proportion of Variance 0.1685 0.1152 0.09933 0.08662 0.07668 0.06305 0.05614
## Cumulative Proportion  0.1685 0.2837 0.38299 0.46961 0.54629 0.60934 0.66548
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.94401 0.90315 0.84528 0.79577 0.76541 0.72853 0.71848
## Proportion of Variance 0.05242 0.04798 0.04203 0.03725 0.03446 0.03122 0.03037
## Cumulative Proportion  0.71790 0.76588 0.80791 0.84516 0.87962 0.91084 0.94121
##                           PC15    PC16    PC17
## Standard deviation     0.63523 0.56479 0.52625
## Proportion of Variance 0.02374 0.01876 0.01629
## Cumulative Proportion  0.96495 0.98371 1.00000
#* Standard deviation: The standard deviation indicates how much of the variance in the original data is captured by each principal component. The first principal component (PC1) has the highest standard deviation of 1.6925, which means it accounts for the most variation in the original data. As we move down the list of principal components, the standard deviation decreases, indicating that each subsequent component captures less and less of the overall variation.

#* Proportion of variance: The proportion of variance indicates the amount of variance in the original data that is explained by each principal component. For example, the first principal component (PC1) explains 16.85% of the total variance in the data, while the second component (PC2) explains an additional 11.52% of the variance. As we move down the list of principal components, the proportion of variance explained by each component tends to decrease.

#* Cumulative proportion: The cumulative proportion indicates the total amount of variance in the data that is explained by each principal component and all of the preceding components. For example, the first principal component (PC1) captures 16.85% of the variance in the data, while PC1 and PC2 together capture 28.37% of the variance. The cumulative proportion can be useful in determining how many principal components to retain for further analysis.


# sample scores stored in cancer_pca$x
# singular values (square roots of eigenvalues) stored in cancer_pca$sdev
# loadings (eigenvectors) are stored in cancer_pca$rotation
# variable means stored in cancer_pca$center
# variable standard deviations stored in cancer_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2
(eigen_cancer <- cancer_pca$sdev^2)
##  [1] 2.8645733 1.9575778 1.6886084 1.4725468 1.3035915 1.0719035 0.9543405
##  [8] 0.8911585 0.8156856 0.7144905 0.6332509 0.5858596 0.5307591 0.5162084
## [15] 0.4035160 0.3189926 0.2769370
names(eigen_cancer) <- paste("PC",1:17,sep="")
eigen_cancer
##       PC1       PC2       PC3       PC4       PC5       PC6       PC7       PC8 
## 2.8645733 1.9575778 1.6886084 1.4725468 1.3035915 1.0719035 0.9543405 0.8911585 
##       PC9      PC10      PC11      PC12      PC13      PC14      PC15      PC16 
## 0.8156856 0.7144905 0.6332509 0.5858596 0.5307591 0.5162084 0.4035160 0.3189926 
##      PC17 
## 0.2769370
# The number 2.8645733 in the first row and first column means that the first principal component explains 2.8645733 units of variance in the data. The number 0.2769370 in the last row means that the 17th principal component explains 0.2769370 units of variance in the data. We can see that the first 7 principal components explain a cumulative proportion of variance of 0.66548, so we might choose to retain those 7 components.

sumlambdas <- sum(eigen_cancer)
sumlambdas
## [1] 17
propvar <- eigen_cancer/sumlambdas
propvar
##        PC1        PC2        PC3        PC4        PC5        PC6        PC7 
## 0.16850431 0.11515164 0.09932991 0.08662040 0.07668185 0.06305315 0.05613767 
##        PC8        PC9       PC10       PC11       PC12       PC13       PC14 
## 0.05242109 0.04798150 0.04202885 0.03725005 0.03446233 0.03122113 0.03036520 
##       PC15       PC16       PC17 
## 0.02373623 0.01876427 0.01629041
# The values indicate that PC1 explains the most variance at 16.85%, followed by PC2 at 11.52%, PC3 at 9.93%, and so on, down to PC17 at 1.63%. These values indicate how much information each principal component carries and can help in determining which components are most relevant for analysis. In this case we can take 7 components for our analysis
cumvar_cancer <- cumsum(propvar)
cumvar_cancer
##       PC1       PC2       PC3       PC4       PC5       PC6       PC7       PC8 
## 0.1685043 0.2836559 0.3829859 0.4696063 0.5462881 0.6093413 0.6654789 0.7179000 
##       PC9      PC10      PC11      PC12      PC13      PC14      PC15      PC16 
## 0.7658815 0.8079104 0.8451604 0.8796228 0.9108439 0.9412091 0.9649453 0.9837096 
##      PC17 
## 1.0000000
# Here, PC1 alone explains 16.85% of the variance, while the first two principal components combined (PC1 and PC2) explain 28.37% of the variance, and so on. This cumulative proportion of variance can be useful for determining how many principal components to include in further analysis. We can see that the first 7 principal components explain around 71.79% of the total variance. 

matlambdas <- rbind(eigen_cancer,propvar,cumvar_cancer)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
##                        PC1    PC2    PC3    PC4    PC5    PC6    PC7    PC8
## Eigenvalues         2.8646 1.9576 1.6886 1.4725 1.3036 1.0719 0.9543 0.8912
## Prop. variance      0.1685 0.1152 0.0993 0.0866 0.0767 0.0631 0.0561 0.0524
## Cum. prop. variance 0.1685 0.2837 0.3830 0.4696 0.5463 0.6093 0.6655 0.7179
##                        PC9   PC10   PC11   PC12   PC13   PC14   PC15   PC16
## Eigenvalues         0.8157 0.7145 0.6333 0.5859 0.5308 0.5162 0.4035 0.3190
## Prop. variance      0.0480 0.0420 0.0373 0.0345 0.0312 0.0304 0.0237 0.0188
## Cum. prop. variance 0.7659 0.8079 0.8452 0.8796 0.9108 0.9412 0.9649 0.9837
##                       PC17
## Eigenvalues         0.2769
## Prop. variance      0.0163
## Cum. prop. variance 1.0000
# Here, the first PC has an eigenvalue of 2.8646, which explains 16.85% of the total variance in the data. The first two PCs combined explain 28.37% of the variance, and the first seven PCs combined explain 71.79% of the variance.

summary(cancer_pca)
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     1.6925 1.3991 1.29946 1.21349 1.14175 1.03533 0.97690
## Proportion of Variance 0.1685 0.1152 0.09933 0.08662 0.07668 0.06305 0.05614
## Cumulative Proportion  0.1685 0.2837 0.38299 0.46961 0.54629 0.60934 0.66548
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.94401 0.90315 0.84528 0.79577 0.76541 0.72853 0.71848
## Proportion of Variance 0.05242 0.04798 0.04203 0.03725 0.03446 0.03122 0.03037
## Cumulative Proportion  0.71790 0.76588 0.80791 0.84516 0.87962 0.91084 0.94121
##                           PC15    PC16    PC17
## Standard deviation     0.63523 0.56479 0.52625
## Proportion of Variance 0.02374 0.01876 0.01629
## Cumulative Proportion  0.96495 0.98371 1.00000
cancer_pca$rotation
##                                 PC1          PC2         PC3         PC4
## GENDER                 0.3210475112 -0.286879473  0.17379787 -0.07237418
## AGE                   -0.0364649541  0.030795541  0.04688999  0.27943243
## SMOKING               -0.0430283442  0.003424731  0.31567559 -0.10751874
## YELLOW_FINGERS         0.3814759828  0.128104954  0.13853036  0.29389320
## ANXIETY                0.4033326977  0.205543431 -0.07469222  0.26312783
## PEER_PRESSURE          0.3069045925  0.105788877  0.22315119  0.15097246
## CHRONIC_DISEASE        0.0902654180  0.066353796  0.10570086 -0.32228900
## FATIGUE               -0.1024499601 -0.391147209  0.29985430  0.20127738
## ALLERGY               -0.2493507498  0.239694551  0.12271547 -0.02157728
## WHEEZING              -0.2442608884  0.124539773  0.26727611  0.32565680
## ALCOHOL_CONSUMING     -0.3321543572  0.413483478 -0.08463899  0.03187039
## COUGHING              -0.2792205789 -0.058744485  0.24960914  0.42897511
## SHORTNESS_OF_BREATH   -0.1417347885 -0.424686551  0.17846341  0.18710306
## SWALLOWING_DIFFICULTY  0.2925413504  0.343624495  0.11855529  0.25354529
## CHEST_PAIN            -0.2335726303  0.316920719  0.02654379  0.06741104
## WEIGHT                -0.0003161562  0.138055198  0.49723646 -0.33025021
## HEIGHT_INCH            0.0485449546  0.155477544  0.49241846 -0.27906767
##                               PC5         PC6         PC7         PC8
## GENDER                 0.20073240 -0.24182352  0.01184223 -0.03985594
## AGE                    0.33787243  0.23970537  0.59890223 -0.53931034
## SMOKING                0.52742230  0.22454151 -0.15463295  0.20038365
## YELLOW_FINGERS        -0.02429773  0.03987572  0.14776817  0.31135018
## ANXIETY               -0.14203498  0.02100195  0.25209607  0.16394901
## PEER_PRESSURE          0.09868719 -0.13237811 -0.39679983 -0.48888049
## CHRONIC_DISEASE        0.34336849 -0.58708763  0.27268807  0.16305791
## FATIGUE               -0.19343265 -0.19872006 -0.17492007 -0.30793949
## ALLERGY                0.06195362 -0.42347967  0.18154792 -0.13304550
## WHEEZING               0.15239622 -0.07376779 -0.30344915  0.23592177
## ALCOHOL_CONSUMING      0.10964754 -0.04578332 -0.04969458 -0.01545999
## COUGHING               0.13819136  0.11156157  0.09656026  0.21956243
## SHORTNESS_OF_BREATH   -0.26321037 -0.22493715  0.29003504  0.21690138
## SWALLOWING_DIFFICULTY -0.08485041 -0.18711304 -0.12109907  0.02088317
## CHEST_PAIN            -0.36362550 -0.22121918  0.06275957 -0.11472139
## WEIGHT                -0.18496760  0.24504959  0.13211070 -0.01887354
## HEIGHT_INCH           -0.28364547  0.18977120  0.11161979 -0.01894483
##                                PC9         PC10        PC11        PC12
## GENDER                 0.281223963 -0.244510475 -0.19864542  0.05106762
## AGE                   -0.181259271 -0.179178546 -0.05135663  0.09966744
## SMOKING               -0.339753798  0.456246291  0.21657468  0.12513209
## YELLOW_FINGERS         0.158443155  0.321656428 -0.15293052  0.26549819
## ANXIETY               -0.025925593 -0.006524112  0.32378188  0.05972929
## PEER_PRESSURE          0.096840684  0.223908923 -0.20262510 -0.31742172
## CHRONIC_DISEASE       -0.258475999 -0.054485578 -0.19258350 -0.03483907
## FATIGUE               -0.196587965  0.100942472  0.31336340  0.29668046
## ALLERGY                0.539524367  0.193301357  0.42374977  0.12050452
## WHEEZING              -0.038620686 -0.568302398 -0.07283366  0.28908157
## ALCOHOL_CONSUMING     -0.031951385 -0.019777592  0.14861759 -0.21687274
## COUGHING               0.309583479  0.133044654 -0.28342941 -0.32037459
## SHORTNESS_OF_BREATH   -0.217039867  0.069598604  0.09520010 -0.35152144
## SWALLOWING_DIFFICULTY -0.312852651 -0.209578384  0.23533684 -0.25912909
## CHEST_PAIN            -0.292637073  0.281207000 -0.49725726  0.21746471
## WEIGHT                 0.003135894 -0.124979041  0.06520556 -0.37197858
## HEIGHT_INCH            0.109288894 -0.106118071 -0.05641311  0.28916542
##                              PC13        PC14        PC15        PC16
## GENDER                -0.15894162  0.55185603  0.36640789 -0.08405264
## AGE                   -0.04778967 -0.01222126 -0.04085982  0.10718595
## SMOKING               -0.17075516  0.24864171  0.03445354  0.03818447
## YELLOW_FINGERS         0.04413678 -0.28524951  0.08772850  0.24449863
## ANXIETY                0.07894326  0.02454333  0.36258509 -0.24996070
## PEER_PRESSURE          0.11049565 -0.16437026  0.05166587  0.26450112
## CHRONIC_DISEASE        0.26824464 -0.30220749 -0.07820030 -0.16153534
## FATIGUE                0.23102739 -0.15679639  0.13579435 -0.35854302
## ALLERGY               -0.27698525  0.00347222 -0.14402150  0.09185413
## WHEEZING              -0.15780709 -0.21356468  0.10523380  0.20530205
## ALCOHOL_CONSUMING      0.47755491  0.19969356  0.50074175  0.13770113
## COUGHING               0.17712228  0.07652517 -0.18263798 -0.45814232
## SHORTNESS_OF_BREATH   -0.01819713  0.11879426  0.04977730  0.51704680
## SWALLOWING_DIFFICULTY -0.12461765  0.28371676 -0.44270428 -0.11953032
## CHEST_PAIN            -0.30203928  0.21227649  0.16091658 -0.11875744
## WEIGHT                -0.33879401 -0.31881843  0.29309129 -0.17393309
## HEIGHT_INCH            0.46330708  0.27552099 -0.26518467  0.16642627
##                              PC17
## GENDER                 0.16314656
## AGE                    0.05623413
## SMOKING               -0.12035893
## YELLOW_FINGERS         0.48817125
## ANXIETY               -0.54709508
## PEER_PRESSURE         -0.29176685
## CHRONIC_DISEASE       -0.07288202
## FATIGUE                0.20916257
## ALLERGY               -0.05062214
## WHEEZING              -0.18401827
## ALCOHOL_CONSUMING      0.29244662
## COUGHING              -0.07868837
## SHORTNESS_OF_BREATH   -0.11319831
## SWALLOWING_DIFFICULTY  0.30009780
## CHEST_PAIN            -0.07706518
## WEIGHT                 0.14740550
## HEIGHT_INCH           -0.15886979
print(cancer_pca)
## Standard deviations (1, .., p=17):
##  [1] 1.6925050 1.3991347 1.2994647 1.2134854 1.1417493 1.0353277 0.9769035
##  [8] 0.9440119 0.9031531 0.8452754 0.7957706 0.7654147 0.7285322 0.7184765
## [15] 0.6352291 0.5647943 0.5262480
## 
## Rotation (n x k) = (17 x 17):
##                                 PC1          PC2         PC3         PC4
## GENDER                 0.3210475112 -0.286879473  0.17379787 -0.07237418
## AGE                   -0.0364649541  0.030795541  0.04688999  0.27943243
## SMOKING               -0.0430283442  0.003424731  0.31567559 -0.10751874
## YELLOW_FINGERS         0.3814759828  0.128104954  0.13853036  0.29389320
## ANXIETY                0.4033326977  0.205543431 -0.07469222  0.26312783
## PEER_PRESSURE          0.3069045925  0.105788877  0.22315119  0.15097246
## CHRONIC_DISEASE        0.0902654180  0.066353796  0.10570086 -0.32228900
## FATIGUE               -0.1024499601 -0.391147209  0.29985430  0.20127738
## ALLERGY               -0.2493507498  0.239694551  0.12271547 -0.02157728
## WHEEZING              -0.2442608884  0.124539773  0.26727611  0.32565680
## ALCOHOL_CONSUMING     -0.3321543572  0.413483478 -0.08463899  0.03187039
## COUGHING              -0.2792205789 -0.058744485  0.24960914  0.42897511
## SHORTNESS_OF_BREATH   -0.1417347885 -0.424686551  0.17846341  0.18710306
## SWALLOWING_DIFFICULTY  0.2925413504  0.343624495  0.11855529  0.25354529
## CHEST_PAIN            -0.2335726303  0.316920719  0.02654379  0.06741104
## WEIGHT                -0.0003161562  0.138055198  0.49723646 -0.33025021
## HEIGHT_INCH            0.0485449546  0.155477544  0.49241846 -0.27906767
##                               PC5         PC6         PC7         PC8
## GENDER                 0.20073240 -0.24182352  0.01184223 -0.03985594
## AGE                    0.33787243  0.23970537  0.59890223 -0.53931034
## SMOKING                0.52742230  0.22454151 -0.15463295  0.20038365
## YELLOW_FINGERS        -0.02429773  0.03987572  0.14776817  0.31135018
## ANXIETY               -0.14203498  0.02100195  0.25209607  0.16394901
## PEER_PRESSURE          0.09868719 -0.13237811 -0.39679983 -0.48888049
## CHRONIC_DISEASE        0.34336849 -0.58708763  0.27268807  0.16305791
## FATIGUE               -0.19343265 -0.19872006 -0.17492007 -0.30793949
## ALLERGY                0.06195362 -0.42347967  0.18154792 -0.13304550
## WHEEZING               0.15239622 -0.07376779 -0.30344915  0.23592177
## ALCOHOL_CONSUMING      0.10964754 -0.04578332 -0.04969458 -0.01545999
## COUGHING               0.13819136  0.11156157  0.09656026  0.21956243
## SHORTNESS_OF_BREATH   -0.26321037 -0.22493715  0.29003504  0.21690138
## SWALLOWING_DIFFICULTY -0.08485041 -0.18711304 -0.12109907  0.02088317
## CHEST_PAIN            -0.36362550 -0.22121918  0.06275957 -0.11472139
## WEIGHT                -0.18496760  0.24504959  0.13211070 -0.01887354
## HEIGHT_INCH           -0.28364547  0.18977120  0.11161979 -0.01894483
##                                PC9         PC10        PC11        PC12
## GENDER                 0.281223963 -0.244510475 -0.19864542  0.05106762
## AGE                   -0.181259271 -0.179178546 -0.05135663  0.09966744
## SMOKING               -0.339753798  0.456246291  0.21657468  0.12513209
## YELLOW_FINGERS         0.158443155  0.321656428 -0.15293052  0.26549819
## ANXIETY               -0.025925593 -0.006524112  0.32378188  0.05972929
## PEER_PRESSURE          0.096840684  0.223908923 -0.20262510 -0.31742172
## CHRONIC_DISEASE       -0.258475999 -0.054485578 -0.19258350 -0.03483907
## FATIGUE               -0.196587965  0.100942472  0.31336340  0.29668046
## ALLERGY                0.539524367  0.193301357  0.42374977  0.12050452
## WHEEZING              -0.038620686 -0.568302398 -0.07283366  0.28908157
## ALCOHOL_CONSUMING     -0.031951385 -0.019777592  0.14861759 -0.21687274
## COUGHING               0.309583479  0.133044654 -0.28342941 -0.32037459
## SHORTNESS_OF_BREATH   -0.217039867  0.069598604  0.09520010 -0.35152144
## SWALLOWING_DIFFICULTY -0.312852651 -0.209578384  0.23533684 -0.25912909
## CHEST_PAIN            -0.292637073  0.281207000 -0.49725726  0.21746471
## WEIGHT                 0.003135894 -0.124979041  0.06520556 -0.37197858
## HEIGHT_INCH            0.109288894 -0.106118071 -0.05641311  0.28916542
##                              PC13        PC14        PC15        PC16
## GENDER                -0.15894162  0.55185603  0.36640789 -0.08405264
## AGE                   -0.04778967 -0.01222126 -0.04085982  0.10718595
## SMOKING               -0.17075516  0.24864171  0.03445354  0.03818447
## YELLOW_FINGERS         0.04413678 -0.28524951  0.08772850  0.24449863
## ANXIETY                0.07894326  0.02454333  0.36258509 -0.24996070
## PEER_PRESSURE          0.11049565 -0.16437026  0.05166587  0.26450112
## CHRONIC_DISEASE        0.26824464 -0.30220749 -0.07820030 -0.16153534
## FATIGUE                0.23102739 -0.15679639  0.13579435 -0.35854302
## ALLERGY               -0.27698525  0.00347222 -0.14402150  0.09185413
## WHEEZING              -0.15780709 -0.21356468  0.10523380  0.20530205
## ALCOHOL_CONSUMING      0.47755491  0.19969356  0.50074175  0.13770113
## COUGHING               0.17712228  0.07652517 -0.18263798 -0.45814232
## SHORTNESS_OF_BREATH   -0.01819713  0.11879426  0.04977730  0.51704680
## SWALLOWING_DIFFICULTY -0.12461765  0.28371676 -0.44270428 -0.11953032
## CHEST_PAIN            -0.30203928  0.21227649  0.16091658 -0.11875744
## WEIGHT                -0.33879401 -0.31881843  0.29309129 -0.17393309
## HEIGHT_INCH            0.46330708  0.27552099 -0.26518467  0.16642627
##                              PC17
## GENDER                 0.16314656
## AGE                    0.05623413
## SMOKING               -0.12035893
## YELLOW_FINGERS         0.48817125
## ANXIETY               -0.54709508
## PEER_PRESSURE         -0.29176685
## CHRONIC_DISEASE       -0.07288202
## FATIGUE                0.20916257
## ALLERGY               -0.05062214
## WHEEZING              -0.18401827
## ALCOHOL_CONSUMING      0.29244662
## COUGHING              -0.07868837
## SHORTNESS_OF_BREATH   -0.11319831
## SWALLOWING_DIFFICULTY  0.30009780
## CHEST_PAIN            -0.07706518
## WEIGHT                 0.14740550
## HEIGHT_INCH           -0.15886979
# The numbers indicate the correlation between each variable and each principal component.For example, in the second table, the variable "SMOKING" has a loading of 0.043 on PC1, -0.003 on PC2, -0.316 on PC3, and 0.108 on PC4. This suggests that "SMOKING" is most strongly correlated with PC3 and weakly correlated with the other PCs. Similarly, "WEIGHT" is strongly correlated with PC3 and negatively correlated with PC4. 

## Sample scores stored in cancer_pca$x
cancer_pca$x
##                 PC1          PC2         PC3          PC4          PC5
##   [1,] -0.646329947  0.332751806 -0.44274023  2.859184418  0.122598754
##   [2,] -0.610508061  0.058855781  0.83878638 -1.618262677 -1.600337930
##   [3,] -0.749550736 -1.504421159  2.66955055 -0.633003311 -0.554423032
##   [4,]  1.096019632  2.420201554 -1.33296429 -0.623882219 -1.620199492
##   [5,]  0.036188930 -1.476567174  1.06322075 -0.297399332  0.877535001
##   [6,] -0.532567242 -1.816704968  1.59490775  0.295408659  1.957759532
##   [7,] -2.543550172 -0.443750841  0.65879801 -0.490274648 -2.164652907
##   [8,]  2.572207921 -0.611692066  0.98184227 -0.400242160 -2.014776748
##   [9,]  1.272938608 -1.748902681 -2.03358144 -0.603715268 -0.190135930
##  [10,]  1.396823254  2.844502270 -1.74624933 -0.548914628 -0.481234509
##  [11,]  2.064989024 -1.179537297  0.77287410  1.619240317  0.200840281
##  [12,] -3.094017924 -0.236356800  0.18223710  0.351212010  1.270144781
##  [13,]  0.217887666 -2.889346007 -0.91100600 -1.432307481 -1.045267875
##  [14,] -3.138457875 -0.373951998 -0.53082600  0.580383563 -1.106225675
##  [15,] -2.644849262  1.404467949 -1.44318316  0.143100628  0.232452899
##  [16,]  1.650628200 -0.224745382  3.27395413 -0.093011818 -0.017887882
##  [17,] -2.832351242  0.682525475 -0.73821564 -0.010801951  0.679269335
##  [18,]  1.926614145  2.783633537 -0.57374848 -1.250303351 -1.057854292
##  [19,]  2.058726013 -1.588839942  1.68092889 -0.276981888 -0.505797399
##  [20,]  0.277622753 -2.858606054 -0.42259847 -2.045803131  0.939549144
##  [21,]  3.229605844 -1.107957864  0.54769701 -1.054795775 -1.494603821
##  [22,]  1.856494117  1.281078425  1.72529424  0.500791276  1.185679005
##  [23,] -0.050480044 -3.127406007 -3.04980327 -1.990025288 -0.705699392
##  [24,] -3.114648178 -0.180587030  0.10426359  0.266726364 -1.323963055
##  [25,]  0.277610744  3.357861077  0.49327829  0.917467589  0.437189391
##  [26,] -0.593103049  0.624184222  0.58814373  2.058674696 -0.508287510
##  [27,]  0.798726715  0.817444755  0.93374653 -0.444838292 -2.523918618
##  [28,] -1.483179713 -1.292781315  1.00754634  0.715640195  0.065334512
##  [29,]  1.135171580  0.783408309 -1.75430086  0.465724163 -0.417313447
##  [30,] -1.513992882 -1.471854090 -0.71445396  1.239531591  0.767188290
##  [31,]  1.249804903 -1.966549418 -1.89456009 -0.936322757 -0.643651435
##  [32,] -1.015659657  1.565562602 -1.96636100  0.688684179 -1.044736566
##  [33,]  1.959456710 -0.179323614 -1.66903462 -0.161407143 -1.632984057
##  [34,]  2.332965976  0.401390187  0.14559217 -1.127745419 -1.393041621
##  [35,]  1.785139801  1.845010472  0.27438022 -1.498888257 -1.437361903
##  [36,]  2.803119610 -0.463091900 -0.61631147 -1.129814399 -0.672500165
##  [37,] -0.906183428 -0.252869061  0.60868898 -0.552044454  0.490794665
##  [38,]  0.625607571 -1.096717211 -0.29615831 -1.482097111  1.247479925
##  [39,] -0.980782008 -0.452929695 -1.00809976 -1.791086031 -0.953341909
##  [40,] -2.531034433  1.054359249 -2.75170356  0.062941767  1.314619757
##  [41,] -1.849943675 -0.036969503 -0.70926167  0.528593229 -1.528261831
##  [42,] -0.768929068  0.787507023 -0.50866975  0.164717527  1.435220054
##  [43,]  1.593703995  0.429036798  1.52983078 -0.546232596  1.925341348
##  [44,] -1.913272210  0.172794143  0.20744605 -0.721150606 -1.789307797
##  [45,]  1.543800949  0.459571313 -1.73845136  0.640217881  2.124908844
##  [46,]  0.292377930  1.094376928  0.98377124  1.985566661 -0.599839321
##  [47,] -0.251600030  0.717276148  0.11116195 -0.575662628 -0.910947467
##  [48,]  0.254838293  0.616454646  0.11114292  1.765377472 -0.055649992
##  [49,]  0.179367433  1.125141361  2.32349723 -0.520119821  0.277971205
##  [50,]  0.952911843  1.162517658 -0.71030972 -2.443376329  1.135427261
##  [51,] -0.851848170  0.904980380  1.94819723 -2.525220801  0.637015235
##  [52,]  0.301087025 -0.841444915 -0.33470279  0.020924532 -0.407424612
##  [53,] -0.906545994  1.108874215  1.03521271  0.179671277 -0.804835301
##  [54,] -1.669956979  0.706463198  0.54089194  0.336371630 -0.952496542
##  [55,]  0.195017025 -0.473764877  0.02002028 -0.520758210  2.360776695
##  [56,]  0.200650077  2.716951889  1.41770341 -0.952121471  0.740632192
##  [57,]  0.518073225 -1.367268061  2.81032243 -0.783212228 -0.937364905
##  [58,] -1.831824121  1.109402015 -0.45190838 -0.415424258  1.192288451
##  [59,]  0.685756178 -0.408794213  0.31395717  0.052650501 -0.299515433
##  [60,] -0.498748639  0.460812608  0.14593215  1.348117096 -1.331297016
##  [61,] -0.851501742  1.873535014  1.07688266  1.057769336  1.654911975
##  [62,]  1.671406217 -0.423441611  0.01975544 -0.908557402  0.637102625
##  [63,] -1.102287719  0.573598828  1.07737079  0.769959205  1.589212310
##  [64,]  0.487489582  1.589885359 -0.52386479 -1.031169208  2.329019058
##  [65,] -1.821523333  0.607204567  2.39323915  0.916516254  0.021873142
##  [66,]  1.890194887  0.314196298  0.21915753  1.943292140  0.447955709
##  [67,] -0.908993115 -1.002601881  2.42194180 -0.792706294  0.098085784
##  [68,] -2.188253111 -1.295291142 -0.20414494  0.389988620 -0.418881441
##  [69,]  1.922127515 -0.483661450 -0.89450174  1.892882896 -0.799898913
##  [70,]  1.831473258 -1.208432390  0.77153641  2.788481409  0.126999960
##  [71,]  1.111645609  2.745232439 -1.90160470  0.587416793 -0.459646651
##  [72,]  1.972055116 -0.866834386  1.97362887  1.622670501 -1.020641169
##  [73,] -3.014541351  0.230927487  1.82358730 -0.870777134  0.323242135
##  [74,]  0.297544932 -3.341535872 -2.66498436 -0.870757883  0.580788533
##  [75,] -3.123513629 -0.202316474  0.02439536  0.353201837 -1.241766589
##  [76,] -2.175119346  0.619405502 -1.87693522 -0.203685676  0.728913726
##  [77,]  0.988165063  0.281111344  2.73257900  1.428695160  0.826564602
##  [78,] -3.171148404 -0.393624263 -0.52860137  0.462431181 -1.108134631
##  [79,]  1.909872378  2.594516335 -1.37039805 -0.316273317 -0.384527514
##  [80,]  1.884232732 -0.836929091  0.25971121  2.107873428 -1.134661282
##  [81,]  0.148410514 -2.759622666  0.17058795 -2.012337053 -0.253735238
##  [82,]  3.159260208 -1.376912455 -0.46218545 -0.031919056 -0.631448204
##  [83,]  1.589202745  3.215922052  1.45544104 -1.156249670 -0.416540691
##  [84,] -0.735262114 -0.558683606  0.06426583 -0.614419304  3.046112719
##  [85,] -2.492696658 -0.248148077  0.57351965 -1.485832190 -0.156211037
##  [86,]  0.164831585  1.067984585  0.76191427  0.778873264 -0.004490012
##  [87,] -0.791080564  1.277284906  0.13896203 -0.512508540  0.424119906
##  [88,]  1.019972886  1.038546046  0.67879987  0.166896049 -1.036950670
##  [89,]  1.355490521  1.048191345 -1.19753355 -1.835391137  0.487381401
##  [90,] -0.217694604  1.268039722  0.47349157 -1.166491895 -0.149140965
##  [91,]  0.200980870  1.569364821  0.23589533 -1.010042731  0.739065292
##  [92,] -1.224091912 -1.370670443  1.95314352 -1.673818763  0.298939223
##  [93,] -1.377079915  1.986294419  0.87166613 -2.146700312 -1.490469516
##  [94,]  1.105509567  1.009068862  0.89835083  0.952703555  1.771596512
##  [95,] -1.763739245  0.521690848  0.52910283 -1.278362192 -1.910301720
##  [96,]  2.144246653  1.031814241  0.70297021 -0.327085070 -1.299959938
##  [97,] -0.247301899  0.219966733 -1.52379872  0.759730600 -0.649174503
##  [98,] -0.943580309 -0.985801589 -2.47162486  0.257887623  0.377111320
##  [99,]  1.434728986  0.425244821  0.30490166  1.146598321  0.613218154
## [100,] -3.084789560 -0.318539996 -0.37773171  0.447133452 -1.342039635
## [101,] -2.211988131  0.291466382 -3.00610005  0.509360032  1.226245309
## [102,]  0.934186102  0.103006060  2.09662512  2.008597406  1.345721614
## [103,] -3.134406710 -0.118005299  0.30107545  0.285470960 -1.220197353
## [104,]  1.829037095  2.049999607 -3.14856312  0.573307112  0.274730687
## [105,]  1.889637650 -0.929392727 -0.06656941  2.287498244 -1.058126770
## [106,]  0.304495611 -2.796890852 -0.22372072 -2.193562275  0.775896724
## [107,]  3.150251750 -1.266687571 -0.15055069  0.047749838 -0.490198468
## [108,]  1.504721972  2.576287720 -0.70174306  0.107804727  0.494154681
## [109,] -0.513569276 -0.429919365  0.66685573 -2.146489489  1.272448570
## [110,] -2.049787993 -0.595265518 -1.39788656 -1.626354625  0.259757990
## [111,] -0.548863117  0.551657627  0.36348773  1.955891473 -0.754455175
## [112,]  0.137370850  1.157565543 -0.22654103  0.220013284 -2.581582640
## [113,] -0.769133382 -1.651851800  2.04076114  0.144667909  0.027932525
## [114,]  1.052948611  1.877461485 -3.18476295  0.436016597 -0.942808927
## [115,] -0.832893079 -1.520043078  1.23238975  0.789310913  1.071200271
## [116,] -0.521560718 -1.774839073  1.77212639  0.062067842  1.766517195
## [117,] -2.590558669 -0.606042808  0.07011790  0.065104794 -1.677476972
## [118,]  2.565856126 -0.636635561  0.90085819 -0.352743399 -1.971483866
## [119,]  1.890132650 -1.553285458 -0.21632974  2.489127348 -0.444483208
## [120,]  1.809485293  2.507239709  0.23379629 -0.904604737 -0.130106958
## [121,]  1.154753405 -0.820601807 -0.18191235  3.258811319 -0.010433839
## [122,] -3.068643554 -0.358110282 -0.17957410  0.278724442  1.079820384
## [123,]  0.603092803 -1.663570228 -0.81847194 -1.742527977 -1.373236514
## [124,] -0.262265717 -0.458918399  1.14583763  0.431171055  0.242487727
## [125,] -2.166676433  1.025027556 -2.44144452 -0.175700086  0.158619707
## [126,]  1.396820173 -1.775823130  0.44315452  0.164190546  1.111925399
## [127,] -2.621538470 -1.080128160 -1.50955976  0.829755886 -1.228986208
## [128,]  1.904628487  2.458422492 -1.72758409 -0.464085245 -0.547767196
## [129,]  2.449232521 -1.233115913  1.14940570  0.807738005 -1.464755784
## [130,]  0.346806820 -2.486510669  0.79296731 -2.700072211  0.411814347
## [131,]  3.029389183 -1.278867895  0.12853282  0.002537778 -1.822456522
## [132,]  1.929414827  1.312693320  1.78007480  0.409498610  0.912824308
## [133,] -0.087138867 -2.322217437 -0.65856528 -1.925296028 -0.156916374
## [134,] -3.286936885 -0.510578871 -1.06794608  1.550312925  0.014328320
## [135,] -0.243063096  3.265766261  0.36303718  0.455074271 -0.101216908
## [136,] -0.885383059 -0.103152291  0.79354384  1.149680047  0.191778725
## [137,]  0.779845934 -1.412199847 -1.48333758  0.232939883 -1.659993771
## [138,] -1.475619881 -1.358995678  0.78667103  0.785254199  0.063938933
## [139,]  1.315156524  1.874152974  1.90819130 -1.745565666 -2.120481240
## [140,] -1.435594309 -0.886655409  1.17170443  0.402456719  0.175080477
## [141,]  0.311554205 -1.503514600  1.98669876 -0.611745934 -0.377702324
## [142,] -1.898169897 -0.689807691 -1.77090536  1.813131302 -0.926438974
## [143,]  1.817982682 -0.274894663 -0.25700981  0.816135845 -1.374023354
## [144,]  1.132188201  0.097406071  1.56257454  1.507813279 -0.597525384
## [145,]  1.041211639  2.476633973 -2.22422610  0.853838815  0.789743107
## [146,]  1.911956582 -1.279682355  0.58493540  2.442926394 -0.412810097
## [147,] -2.208254898  0.244829063  1.39493556 -0.446948312 -0.084142771
## [148,]  0.199618587 -1.606668229 -0.56648477  0.211079060  1.819639955
## [149,] -3.151824202 -0.105442765  0.28680901  0.530946496 -0.974148171
## [150,] -2.581152399  1.660530129 -0.45658460 -0.913041511 -0.642489672
## [151,] -1.821212050  0.049106818 -0.42528735  0.326193983 -1.727503000
## [152,] -0.709027954  1.118219938  0.61257539 -0.562639222  0.859330817
## [153,]  1.527353442 -0.054701131 -0.07747901  0.328574008  2.559335815
## [154,]  0.134446169  0.264009802 -1.70348774 -1.428607876 -0.536373103
## [155,]  2.379419131 -0.094554298  0.55507534 -2.767771658  0.132335453
## [156,]  1.816004356  0.546117886 -3.21264766  0.454846344  0.862978356
## [157,]  0.693446059  0.977045613  0.26008812 -3.763916185 -2.021635959
## [158,]  1.637082331 -0.335000397 -2.05755169 -0.746108139 -0.416159349
## [159,]  0.296933463  1.194165867  2.60436670 -1.181630957 -0.546751798
## [160,]  0.822754284  0.670235764 -2.41335728 -1.103663683  2.312033587
## [161,] -0.918911402  0.663806963  1.18690797 -2.128116926  1.024959096
## [162,]  0.231900961 -1.270641543 -1.76967126  0.862961366  0.236368161
## [163,] -1.013939681  1.262821648  1.47304856  0.585206501 -0.098566521
## [164,] -1.772694007  0.767271176  0.63712578  0.973149028 -0.128283972
## [165,]  0.113097963 -0.357041885  0.30262585 -0.029388012  3.038456413
## [166,]  0.075576812  2.276081375 -0.14913244  0.428758735  1.958389064
## [167,]  0.477358107 -2.002383447  0.60892730  0.553159679 -0.100163895
## [168,] -1.789229364  1.010323518 -0.71414648 -0.663628669  0.826928708
## [169,]  0.719595969 -0.266957041  0.81937861 -0.376044152 -0.660229054
## [170,] -0.479345237  0.029424455 -1.25225042  1.746517856 -1.293222426
## [171,] -0.706487604  1.979788355  1.48164274  0.256635741  0.659195101
## [172,]  1.659264316 -0.669984273 -0.80889570 -0.497190062  0.868951875
## [173,] -1.053631487  0.418816948  0.64807542  0.512000760  1.171296835
## [174,]  0.439619994  1.347267284 -1.34471999 -0.491319346  2.768031869
## [175,] -1.736485551  0.889505297  3.31946123  0.301066951 -0.567055601
## [176,]  1.908193822  0.100984757 -0.40588659  1.869485714  0.234457926
## [177,] -1.025193951 -1.347023632  1.14815308  0.528994073  1.290656942
## [178,] -2.229264288 -1.622311063 -1.29643165  0.990124308  0.004899612
## [179,]  1.957225328 -0.433792361 -0.55469125  1.069085426 -1.511190662
## [180,]  1.838526733 -1.356872831  0.31115872  2.847776221  0.079447061
## [181,]  1.180112751  2.940457687 -1.22406253 -0.005852669 -1.024121550
## [182,]  1.811861750 -1.441142807  0.01690577  3.101211177  0.312426585
## [183,] -3.110670459 -0.364952154 -0.24358794  0.575227017  1.429197339
## [184,]  0.360229263 -2.696506149 -0.58357746 -1.726264724  0.050562343
## [185,] -3.223541067 -0.179218190  0.09257126  0.673772079 -0.685860956
## [186,] -2.269746579  0.759892939 -1.50517585  0.258232091  1.433596248
## [187,]  2.747577269 -0.892695063  0.37334010 -0.956311448  1.532003894
## [188,] -0.149697264 -1.642331214 -2.28814301 -1.471419303 -0.781235965
## [189,]  2.400777592  0.347128955 -1.71026348 -1.021489585  0.434261725
## [190,]  2.664155409 -1.393549647 -1.71837991  0.529051941  0.057805594
## [191,]  0.613534144 -1.458382780  0.89659577 -3.179203564  1.045150296
## [192,]  2.833005133 -1.403952109 -1.83872171 -0.412027674  0.480801518
## [193,]  3.117056920 -0.179410694 -1.10177848 -1.856855416  0.106854315
## [194,]  1.396552964 -0.642255545  0.02050933 -3.110585372  1.836705087
## [195,] -2.512642306  0.003850388  1.41044718 -1.765460899 -0.188561541
## [196,]  0.041302770  0.619388750 -0.80700898  2.078283851  1.142567875
## [197,] -0.813244847  0.880928753 -1.22887662  0.288977960  0.912007999
## [198,]  0.986709032  0.840164793  0.05264538  0.423153898 -0.837258657
## [199,]  1.252252204  0.988451934 -1.42301728 -1.323117294  1.159512551
## [200,] -0.137885258  1.481731866  1.13219939 -1.525196202 -0.559153131
## [201,]  0.136542296  1.207505130 -0.99116369 -0.216929658  1.363785406
## [202,] -1.270419897 -2.048452421 -0.26872446 -0.709046147  0.847964695
## [203,] -1.511779573  1.885698680  0.38947345 -1.030942437 -0.282150752
## [204,]  1.085397022  1.243127916  1.68487628  0.664169343  1.724253118
## [205,] -1.937338444  0.418609362 -0.03359575  0.232284332 -0.284578291
## [206,]  2.079880884  0.956433882  0.49279972 -0.166467991 -1.020841607
## [207,] -0.238660237  0.398472349 -1.03260961  0.864147837 -0.508793937
## [208,] -0.159651843 -1.132594137 -0.05598138 -1.013129749 -0.784261739
## [209,]  1.500566250  0.840189583  1.66536450  0.435082161  0.072426854
## [210,] -3.014209221  0.355964728  1.96591223 -1.080854377 -2.396209206
## [211,] -2.105058072  0.929924423 -0.80062808 -1.017803085  0.046453380
## [212,]  0.942418911  0.054526904  1.96648773  1.934291974  1.240767541
## [213,] -3.148924082 -0.594610120 -1.31041545  1.087399067 -0.793683557
## [214,]  1.878394695  2.398574133 -1.99024350 -0.062447648 -0.190863682
## [215,]  1.966715740 -0.630957885  1.05402026  1.155588169 -2.010604775
## [216,]  0.277041266 -2.759604202 -0.07945444 -2.231880620  0.846800791
## [217,]  3.171498795 -0.995402267  0.71278740 -0.251134699 -0.651266456
## [218,]  1.556928786  2.591469129 -0.66355483 -0.035006615  0.235938143
## [219,] -0.616500433 -0.513737474  0.21506585 -1.061891800  2.369939157
## [220,] -2.586211894 -0.187369377  0.72652260 -1.088595931  0.457090666
## [221,]  0.137716815  0.366509534 -0.16792988  0.543739987  0.849702117
## [222,]  0.865093182  0.844185218 -1.74842823 -1.798595288  1.737694179
## [223,] -0.913971012  0.969266395  1.97298215 -1.716775781  1.472684147
## [224,]  0.313977949 -0.945041768 -0.72531396  0.292773295 -0.288118442
## [225,] -1.072776501  0.599121897 -0.68085976  1.492600012  0.450812463
## [226,] -1.699472023  0.930082069  1.24714633  0.260609994 -0.813935347
## [227,]  0.251825578 -0.075337937  1.19428496 -0.695732642  2.249570554
## [228,]  0.014567830  2.117497330 -0.74689429  1.102971967  2.580198736
## [229,]  0.504752774 -1.860630264  1.15079860  0.009577708 -0.529532914
## [230,] -1.698692239  1.131623356 -0.33312414 -1.038468810  0.327760281
## [231,]  0.558690456 -0.191830970  0.83866091  0.887454211  0.824592143
## [232,] -0.464475998  0.564705610  0.54205784  0.907998903 -1.720403026
## [233,] -0.736607022  2.290777684  2.53098650 -0.131746814  0.602622034
## [234,]  1.791907070 -0.482831255 -0.20730594 -1.103593125  0.098407869
## [235,] -1.021622690  1.026768352  2.49920628  0.201024453  1.131623848
## [236,]  0.511871527  1.643341139 -0.30949731 -1.318210021  2.062253193
## [237,] -1.857682768  0.067118102  0.65282615  1.571807247  0.370261802
## [238,]  1.973432877  0.329461293  0.39577264  1.190688519 -0.369711578
## [239,] -0.844025398 -1.043350556  2.43615654 -1.497678287 -0.655538378
## [240,]  1.798603632  1.277822318  1.64041006  0.964305961  1.712072698
## [241,]  0.567970913 -1.465901428 -1.40821954 -1.475588124  1.328585265
## [242,] -3.128591618 -0.100406746  0.42598650 -0.002631206 -1.449540091
## [243,]  0.921300172  2.566347959  0.08444693 -0.327261230 -0.277565465
## [244,] -0.707766669 -0.140351712  0.50896513  0.494931879  0.794661098
## [245,]  0.727027732 -1.433071548 -1.59685113  0.593875654 -1.235796634
## [246,] -0.813209418 -1.199505257  0.40464481 -0.405256608 -0.735537650
## [247,]  1.137562086  1.419593842  0.28112686 -0.123186538 -0.567331492
## [248,] -1.568549443 -1.353854798 -0.38152350  1.471266594  1.164907662
## [249,]  0.206337661 -1.720761209  1.11360977  0.581416058  0.745153770
## [250,]  0.582400965 -1.654341741 -4.03720871  0.592072897  0.127026158
## [251,]  1.852485410  0.064395647  0.86057895  0.277190722 -1.725563610
## [252,]  1.069824793  0.099379354  1.64192217  1.436102237 -0.464752520
## [253,]  1.320083419  3.019301770 -0.60379759 -0.838972788  0.575723760
## [254,]  1.826416008 -1.528447714 -0.21991298  2.977344774  0.131843922
## [255,] -2.295131492  0.231836563  1.14798587  0.601866665  0.972169398
## [256,]  0.184324517 -1.188753076  0.66614989  0.264048756  2.108122913
## [257,] -3.143108851 -0.334761125 -0.41121557  0.580820285 -1.073009725
## [258,] -2.658851944  1.282851605 -1.79186198  0.149784893  0.220653288
## [259,] -1.871308247 -0.027948405 -0.67512508  0.569331753 -1.428769300
## [260,] -0.711591973  0.787827363 -0.51712533  0.015709149  1.149714717
## [261,]  1.686997211  0.200537154  0.82927435 -0.749102450  1.380292709
## [262,] -1.858110215 -0.038377392 -0.44768335 -0.780682656 -2.102146836
## [263,] -0.009983675 -1.961070989 -0.67218900  0.977524185  1.756913624
## [264,] -0.640492349 -2.449177339 -0.47626302  1.394993461  2.816254162
## [265,] -2.667743902 -0.624537600 -0.07078989  0.631216256 -1.022190383
## [266,]  2.455060778 -0.932060495 -0.13446506  0.605103847 -1.049802875
## [267,]  1.289042304 -1.784059560 -2.00134352 -1.157706179 -0.679250082
## [268,]  1.464834078  3.334018842 -0.17613207 -1.228668742 -0.968154666
## [269,]  2.198079582 -0.920094403  1.60613778  0.943922005 -0.588805903
## [270,] -2.876746306  0.339743512  2.19185099 -1.486040419 -0.507401063
## [271,]  0.060055521 -3.317302160 -2.37218122 -0.195895671  0.166259201
## [272,] -3.142504794 -0.257942521 -0.17738398  0.552812520 -1.059087544
## [273,] -2.634807935  1.168554355 -2.23638980  0.468363114  0.337151628
## [274,]  1.505301199 -0.740318106  1.46628345  1.427782791  1.331421460
## [275,] -2.740709424  0.722367627 -0.45692349 -0.908981952 -0.263057377
## [276,]  1.905774831  2.562920015 -1.43666755 -0.402881750 -0.453816513
## [277,]  2.017633169 -1.986659604  0.38967132  0.286357120 -0.144177349
## [278,]  0.099735552 -2.950607582 -0.86988372 -0.826878661  2.360250992
## [279,]  3.015656624 -1.371646389 -0.56504871  0.865577325  0.487728246
## [280,]  1.825438683  0.837995677  0.24336244  1.242694873  1.631988024
## [281,] -0.131569292 -2.296085695 -0.47529079 -2.174913004 -0.202269462
## [282,] -1.322834911 -1.037008743 -0.41131805 -1.699174863 -2.575108219
## [283,]  1.736775731  1.283284999 -1.49919175 -0.917952163 -1.119800076
## [284,] -0.592930367  0.224645288 -0.78024226  2.755903856 -0.168581495
## [285,]  1.928894090  2.708029329 -0.86288820 -1.014020749 -0.920456081
## [286,]  2.367428208 -1.947699135 -1.30903111  2.358687696 -0.378804689
## [287,]  0.290098251 -2.530916123  0.71152818 -2.701725928  0.558829150
## [288,]  3.070879292 -0.884056499  1.49195594 -0.861410776 -2.416739566
## [289,]  1.901858849  1.316866466  1.83316729  0.347207053  0.949670177
## [290,] -0.148458186 -2.510569491 -1.25163372 -1.591987828  0.190570397
## [291,] -3.160670480 -0.142895407  0.08071687  0.912125001 -0.674116273
## [292,] -0.350752444  2.762553158 -1.29900566  1.452158009  0.740670485
## [293,] -0.898366238 -0.174979956  0.55300720  1.296536856  0.308268936
## [294,]  0.861502720 -1.425901982 -1.64547390  0.420718507 -1.767384879
## [295,] -1.473211209 -1.294127913  1.01677328  0.634936076 -0.026911060
## [296,]  1.111453285  0.841309250 -1.52709178  0.333852745 -0.419205639
## [297,] -1.529405423 -1.178528936  0.25100317  0.921255092  0.711687244
## [298,]  0.258107397 -1.743891382  1.19553857 -0.139263124  0.027543069
## [299,] -1.904656129 -0.528637935 -1.18196439  1.415971336 -1.132951811
## [300,]  1.848956846  0.029663156  0.79616089  0.147726816 -1.830864913
## [301,]  1.150509115  0.284559833  2.21074344  1.095715426 -0.877160551
## [302,]  1.152918867  3.108695777 -0.10406543 -0.443281716 -0.231421332
## [303,]  1.932277477 -1.124180447  1.11643983  2.110205036 -0.653007261
## [304,] -2.222289178  0.217516381  1.31604101 -0.408380875 -0.025831892
## [305,]  0.309135098 -1.125563191  1.01347625 -0.729745122  1.004636281
## [306,] -3.290318919 -0.773981843 -1.92760392  1.864300336  0.137285445
## [307,] -2.664442991  1.297484746 -1.64793851 -0.204320402 -0.026482672
## [308,] -1.831829290  0.042083823 -0.43588975  0.322802182 -1.701712188
## [309,] -0.648431973  1.114788359  0.51649880 -0.439377745  0.770588458
##                  PC6           PC7          PC8          PC9          PC10
##   [1,]  0.7182594090  0.0900371245  1.051744451 -1.937650817  0.4989633841
##   [2,] -0.6772550951  1.9777064114 -1.557168739 -1.216866754 -0.5305604825
##   [3,]  1.1916488129 -1.2195053227 -0.411285727 -0.323523971 -0.1148162874
##   [4,]  1.7403584683  0.6091639642  0.258612735 -0.654105790 -0.2130147794
##   [5,]  2.1847893962  0.2198466952  1.845426766  0.627204075 -0.6014890431
##   [6,] -0.2480383908  1.4550678660  0.483870124  0.558138013 -0.2014692509
##   [7,]  0.9965416546 -0.8530147261  0.684045214 -0.285018564 -0.7811912336
##   [8,] -0.5055130553 -0.4251606584 -0.227317424  1.333349131  0.1917601304
##   [9,]  1.1709683751  0.1970313925 -1.162926497  0.312410711 -1.0231229714
##  [10,] -1.4206369931 -0.3235588013  0.045516341  0.241215288  1.0354175725
##  [11,] -0.9877439635 -0.2335341620  0.675723070 -0.141706192 -1.1092713774
##  [12,] -0.7610221388  0.7783351846 -0.103927236 -0.972945187  0.3836599781
##  [13,]  0.7356356660 -0.1182467785 -0.538078442  0.115259335 -0.8498243779
##  [14,] -0.3303380494 -0.4144204301  0.078712304  0.509575391 -0.1786395470
##  [15,]  0.8668959754  0.1542886143 -0.441232526  1.201097550 -0.7763798784
##  [16,] -1.0582597188 -0.7242179155  1.600738198  0.810017235  0.0978269150
##  [17,] -0.5049244711  1.7816022095 -0.061502145  0.001210227 -0.9101287848
##  [18,]  0.1840838476 -0.0442652608 -0.003095435 -0.819714203  0.2257921571
##  [19,]  0.4184360878  1.5182832851 -0.362960279  0.678886989 -0.0700320345
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## [195,] -0.0361418701  1.1940454863 -0.056101725 -0.572886618  1.2842161588
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## [197,] -0.4171954059  1.9082983690  1.570395017 -0.118208163  2.1876612889
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## [200,] -1.9391008388 -1.5916732020 -1.358576237  0.258672413 -1.3882423287
## [201,]  0.5061086374 -2.2539731423 -0.817921519 -1.074066868 -0.7613814886
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## [204,] -0.6194051296  0.5711016494  1.141953344  0.694678859 -0.3218729187
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## [206,]  1.5353342036 -0.8566145090 -0.870725157 -1.469063084  1.4447359764
## [207,]  0.2843473182  2.3606655844  0.276786804  1.619469616  0.5927392689
## [208,]  2.1082846487  0.0794758735 -0.565386610  0.756200838 -0.1403342114
## [209,]  1.6773717584  0.0450418316 -0.809086210  0.807831385  1.3302258702
## [210,]  0.6991278108 -0.0095894399  0.179769365  0.836207202 -0.7043745674
## [211,]  1.2541072676 -0.8600370530  0.744939979  2.134547447 -1.2090722109
## [212,] -1.2882696167  1.1553962021 -0.476224826 -0.669127906  0.3736588436
## [213,] -0.7026680506 -0.6172392913  0.108360098  0.480835278  0.0133481689
## [214,] -0.3097785811  0.0864806846 -0.407527603 -1.022680111  0.4325845747
## [215,]  0.3030799705  0.1932021189 -0.391930040  0.002912519  0.4835420076
## [216,]  0.0884210532  0.2639798854  0.060627755 -1.184750704 -0.0865438470
## [217,] -0.5076065148  0.8397193769 -0.672936226 -0.646734882 -0.5770894616
## [218,] -1.9000416601 -0.6517011170  0.235922306  0.709875493 -0.6982881326
## [219,] -0.3537816061  0.8331990739 -0.634960319  0.992090639  0.6400768789
## [220,] -0.1420316905  1.5292124380 -0.488210514 -0.825313721  1.2978894992
## [221,] -2.7715548775 -1.1711189217 -0.224810404 -1.292249361  0.1126633235
## [222,]  0.9478196676 -0.5524772989 -0.253200914 -0.863825131  0.5535381578
## [223,] -0.3074748126  0.0308155105 -2.454120724 -0.296762847 -0.6126684205
## [224,] -1.0298320649  1.0206780718  0.855237899  0.215226261 -0.5046193620
## [225,] -1.2212535442 -1.9376653665 -1.617638308  0.884574081 -0.6814473948
## [226,] -1.7503323526 -0.6239726748 -0.629460887 -0.312870598 -0.4785053719
## [227,] -0.0392305174  0.2615016712 -1.130505607  1.396462056  1.2579694919
## [228,]  0.2225209433  0.8615858150  1.402180848  0.064659209 -0.2595934931
## [229,]  0.7412912740 -0.8531850969 -0.013240528  0.088707514  2.0467880852
## [230,] -0.7891935436  0.5454448937  1.084975113 -0.692704938  1.1037826112
## [231,] -0.2848528400  0.0915404055 -0.959288153 -2.908879872  0.2430427710
## [232,]  0.3190198692  0.8987541821 -0.848630395  0.972090818  1.6721437422
## [233,] -0.3048533945 -0.8294496564 -0.274188663 -0.289207469  0.6960047812
## [234,]  2.2580891391 -0.3672360792  2.171436426  1.635181116  0.7586462447
## [235,]  2.2292543596 -0.0922318122 -1.411306251  1.281549337  0.2631799499
## [236,] -0.3527796009  0.1126639646  0.675632513 -0.094287409 -1.7323666455
## [237,] -0.0255121956 -0.9127629007 -0.187010389  0.243044661  1.7805492648
## [238,] -1.2341259405 -1.2470149473  0.454072898 -0.011152504 -0.5126806365
## [239,] -1.2742061293 -0.8500378489  2.645838204  0.780696755  0.9179201758
## [240,]  1.5845528807  0.3445231282 -0.272478651  1.454825603 -0.6233202025
## [241,] -1.1153339245  0.9284920103 -1.425772808  0.817089168 -0.3921075456
## [242,]  0.1514350674 -0.0946406719 -0.023153129  0.525905682 -0.4341328443
## [243,]  0.1200518159  2.0631355943 -0.104296840 -0.338243733 -1.3731108572
## [244,]  0.2027959021 -0.0849401635  1.463003500 -1.950875326 -0.9218141608
## [245,] -0.7978352078  1.1938858224 -0.299961432  0.614450844  0.9101726144
## [246,]  0.7396572613 -1.8187328378 -0.722086197 -1.493394128  0.4645379441
## [247,] -0.2925104736  1.7654731385  0.900472570 -1.224373692 -1.9931934779
## [248,]  1.5528942911 -0.3823914320  1.036454458 -0.647625094  0.3524471733
## [249,] -1.3878602134  0.1146013481 -0.164370679  1.656090276 -0.3786438121
## [250,]  0.8920970829 -0.2471013297 -1.020127228 -0.368418686 -0.1360227207
## [251,]  0.5619597323  0.8961292302 -1.334701366  0.379131211  0.2574922605
## [252,] -1.9119232499  0.6272419580 -0.040167086  0.267890918 -0.3638157824
## [253,] -0.6003662352 -0.0860071646  0.036601334 -0.492122827  1.7173048359
## [254,] -0.0075139193 -0.5445206700 -0.012862474  0.166851359 -0.9379488813
## [255,] -0.3317993324  1.3861884739  0.366675439 -0.608606841  0.8330237465
## [256,] -0.1633623299  0.3209166774 -1.432590791 -1.371786484 -0.0640701133
## [257,] -0.2232857151 -0.2414764424 -0.056790620  0.475449978 -0.2479260376
## [258,]  0.6025818559 -0.2811734954 -0.100457057  1.230327282 -0.5999538620
## [259,]  0.4170038534  1.6903016657 -0.874392374  0.326717780  0.5784111216
## [260,]  0.0002427880 -2.7793829806 -1.102881662 -0.225616264 -0.1222536990
## [261,]  0.1823409035 -1.1936153031  0.214544196 -0.186836394 -0.3278446880
## [262,] -1.2715304280 -2.7286452138 -0.103067971  0.538373097  0.3577129850
## [263,]  1.4670339885  0.0560863487  1.649570038  0.463640188 -0.2575170414
## [264,] -1.2367743349  0.6690005850  0.825026937  0.357533884  0.3547903089
## [265,]  1.1603304648  0.2564488286 -0.466493609 -0.784972182 -0.9809742273
## [266,] -0.7338553859 -0.0482649295 -0.773772879  0.957953335  0.2606999512
## [267,]  0.8889099300 -0.7066213845 -0.312820562  0.509747636 -0.7811957618
## [268,] -0.5705395526  0.5542518386 -0.472892785  0.313815624  0.5342072708
## [269,] -0.8512332042 -0.4827810745  1.036359939  0.228757735 -1.1577294509
## [270,] -0.3740756655  0.0417266096  0.932044033 -0.273332092  0.2768452963
## [271,]  0.4032019324  0.2527873889 -1.136724346 -0.363677374 -0.7277646423
## [272,] -0.0441355087  0.0294030664 -0.262150079  0.441155012 -0.3627821102
## [273,]  0.3577792653 -0.4086229346 -0.083707788  1.279164475 -0.4796391971
## [274,] -1.5531806436 -0.3803915162  0.949686923  0.343125451  0.2926302275
## [275,] -0.8756634804  0.4962594512  1.171716745  0.439440455 -0.5907452008
## [276,] -0.0669921990  0.2226560485 -0.428683876 -0.958918591  0.3034629867
## [277,] -0.3019960188  0.7735920022  0.079229910  0.654463086  0.3520907959
## [278,]  0.4308091328  1.8659576704 -1.545778625 -1.887880264 -0.4217303502
## [279,] -0.7519674960  1.2586366080 -1.278552065 -1.119937175 -0.5003505269
## [280,]  0.5227459304 -1.1517873688  0.828307407  1.701901555  0.0377575323
## [281,] -1.2891964728  0.7268513687 -0.413380030  0.633575030 -0.5561705670
## [282,]  0.0072723101  0.1177275082 -0.650013848  0.271424375  0.5749921706
## [283,]  1.3745317270 -1.0682943337  1.842989199 -0.939231198  1.3300725948
## [284,]  0.3001583816 -0.6476922795  1.653718382 -1.711975445  0.7720718709
## [285,]  0.0608953430 -0.0522280140 -0.057624847 -0.829450762  0.2804388426
## [286,] -0.3793650617 -0.7280509615  0.123139185  0.461371200  0.5299479216
## [287,]  0.4851285995  0.5384871928 -0.034959347 -1.162760972 -0.2992416890
## [288,]  0.7206171053 -0.5881867306  0.011350392  0.249568814 -0.3876300550
## [289,]  1.2655471357 -0.6204720310  0.636573907  1.855271946 -0.3714336955
## [290,] -1.6098224177  0.6667855015 -0.514808749  0.565964376 -0.4048883452
## [291,]  0.3830414208  1.0109341013 -1.123266595  0.241569021 -0.6783633899
## [292,] -0.6782178362  1.3000455823  0.767054107  0.198642605 -0.6140196286
## [293,]  1.6844910775 -0.0002079914  0.603823492 -1.555022296 -1.0310973402
## [294,] -1.1399821131  0.5706408517  0.225131480  1.006080236  1.1212419211
## [295,]  1.2939157922 -1.0000212360 -0.805579220 -1.173390048  0.5219335656
## [296,] -1.5209166720  0.1111558629  2.082635517 -1.083053578 -1.2292044177
## [297,]  1.7354934370 -0.5086166346  1.274213378 -0.507815962  0.2828894521
## [298,] -1.7703871607 -1.0686169716  0.945636813  1.981196497 -0.0611704156
## [299,]  0.6019869525 -0.0363752051  0.421560655 -0.836265536 -0.6174102949
## [300,]  0.4477745716  0.6016858070 -1.070264315  0.420841396  0.3475341540
## [301,] -1.7409282983  0.6768220842  0.003313970  0.460084373 -0.4587245723
## [302,]  1.0154864475 -0.0985800207 -0.643518629 -0.004429237  1.5584108132
## [303,]  0.4923718799 -0.3707895537  0.066845323  0.432132091 -1.1977180848
## [304,] -0.8242134745 -0.2005517233  1.866263998 -0.162230166  1.2491918924
## [305,] -0.5806708637 -1.0993056715 -0.071064434 -0.836025698  0.2882833788
## [306,] -0.5943934264  0.1107253930 -0.653395882  0.019173765 -0.1081640853
## [307,]  0.5500102538 -0.6588696646  0.287068731  1.294093947 -0.5254052273
## [308,]  0.4272639574  1.5292324864 -0.687199135  0.451762489  0.5889517563
## [309,]  0.5268382605 -2.2511204799 -1.404420153 -0.130277486 -0.4341384337
##                PC11          PC12         PC13         PC14          PC15
##   [1,]  0.420523565  0.4334820544  0.016896184  0.568431041  0.4383575733
##   [2,]  0.462308125  0.3986804449 -0.218844308  0.061830934 -2.0687208915
##   [3,] -1.315721292 -0.6118901582 -1.234182675  0.374500028  0.7773050725
##   [4,] -0.036031283 -0.2638657935 -0.338447239  0.010300783  0.5421504516
##   [5,] -0.912182701 -0.4352120930 -1.415924824  0.029107293  0.2282780957
##   [6,]  0.006675664  1.2983623838 -0.206751142 -0.234096001 -0.6232337130
##   [7,] -0.681612182 -0.4367979407  0.627895778 -0.126860747  0.5778337358
##   [8,]  1.570297126 -0.3494589711 -0.224076737  0.307935702 -0.1791024816
##   [9,]  0.588029356  1.3889527245  0.379929206  0.698899496  0.2331253689
##  [10,]  0.013843135 -0.3935900740  0.183078896 -0.531951622 -0.0795574606
##  [11,] -0.393455043 -0.8581065623  0.256269265 -0.857916040  0.0129291768
##  [12,]  0.012211427  0.7468853985  0.391100484  0.158685593 -0.2626260427
##  [13,]  0.249502857  0.0929055090 -0.044637030  0.616334219 -0.0808919597
##  [14,]  0.108202924  0.0621200579 -0.074766804 -0.009759719  0.1656639689
##  [15,] -0.894184802  0.6667391909 -0.134044309  0.395128230 -0.5965953711
##  [16,]  0.908454725 -0.2179462237  0.185976081 -0.004498742 -0.4711337983
##  [17,] -0.992433913 -0.7479697500 -0.485089739 -0.584556336 -0.1028938720
##  [18,] -0.796874258 -0.9948424816  0.538850685 -0.867448372  0.4749865902
##  [19,] -0.844001807 -0.4463708756  1.628548810 -0.604924292  0.2536040792
##  [20,]  0.320441162  0.1598941284 -0.096108696  0.385799068 -0.0495534724
##  [21,]  0.467789803 -1.2219438435  0.249408139 -0.731181079  0.4061416274
##  [22,]  0.411759401 -0.2953011717 -1.528031755  0.251766287 -0.3967280920
##  [23,]  0.951863976 -0.0769681900 -0.219517073  0.120893372 -0.3421600285
##  [24,]  0.095539826  0.0651550583  0.029651045 -0.012197733  0.1471579650
##  [25,] -0.734840381 -0.7561054781 -0.278001541 -1.273542765  0.0662511665
##  [26,]  0.494253801  0.0829017276 -0.087042222  0.335995178  0.6686192208
##  [27,]  1.219675724  0.3473208400 -0.118633159  1.409979591  1.0286389588
##  [28,] -1.041488146 -0.2161509584 -0.829347522 -0.448322267 -0.2646588750
##  [29,] -0.837946225  0.2926483701  0.133017998  1.000956763  0.8888048793
##  [30,]  0.404992386  0.1465291483  0.689510060 -0.526647777  0.4152453066
##  [31,] -0.863377283  0.8313440043  0.490013777  1.143399608 -0.8880189012
##  [32,]  1.135636716 -0.4148927197 -1.304990553  0.638676216  0.2022641052
##  [33,]  0.828808911 -0.6314252501 -0.319879928 -0.179981187 -0.9960511402
##  [34,] -1.045951865  0.0668733975 -0.398041733  0.851525389 -0.2799188786
##  [35,]  0.009148572  0.9825179146 -0.693330830  0.687387035 -0.9228988259
##  [36,]  0.003684991 -0.4452323697  0.131529168  0.435770915 -0.5539587221
##  [37,] -1.864892347 -0.2768934238 -1.318510710 -1.321186730 -0.2473171349
##  [38,] -0.021480573 -0.3037972350 -0.919328509  1.015139336 -1.1288114460
##  [39,] -1.480099028  0.0080071951 -0.864049795 -0.975689884 -0.4962413909
##  [40,] -1.149182018  0.1416856598 -0.300607468 -0.552503014 -0.3531137163
##  [41,]  0.806124346 -0.1179494334  0.638998799  0.611840391  0.4739033034
##  [42,]  2.023023934 -0.1990796775 -0.721549002 -0.445591628 -0.3057797375
##  [43,]  0.118601406  1.1488752332  1.127125769 -0.819164504  2.0210436648
##  [44,]  0.370000163 -0.3286131012 -0.391529217 -0.756123983  0.9131450099
##  [45,] -1.614973464 -1.2134306509  1.337189896  0.479254455 -0.7940825244
##  [46,] -0.822660699 -0.5381476425  1.351054267 -0.871938739  0.2867008044
##  [47,] -0.825820015 -1.4698517789 -1.565778171 -0.912485003 -1.6294596013
##  [48,] -1.665852215  0.3708029720  0.525802391  0.726885898  0.2313883640
##  [49,]  1.008512627 -0.1394632519 -0.443699967  0.933724085  1.2044084929
##  [50,]  0.400890266 -0.8467778863  1.276292343 -0.515240987  0.6590492803
##  [51,] -0.203704842  0.7304241801 -0.305652649  0.014290211  1.4018728347
##  [52,]  1.318968269  1.2676593358 -0.089367897 -2.200932157 -0.0105380974
##  [53,] -0.471740318  0.0747768687  0.312992783  1.462436004 -0.3283840429
##  [54,] -0.248509625 -0.7626119578  1.151848027  0.102037854 -1.1656168492
##  [55,]  0.059631997 -0.3422837836  0.631467132 -0.430910715  0.7213219035
##  [56,]  1.187959690 -0.3529930654  0.325920926 -0.635921694 -0.3963700610
##  [57,] -1.516700646 -0.5463492685 -0.689798999  0.290699987  0.6539578856
##  [58,]  0.063045575 -1.5632941214 -0.689317295  0.965257941 -1.1668081449
##  [59,] -0.585555242  0.3180404088 -0.613800091 -1.021079901 -0.7911169580
##  [60,]  0.168377749 -0.6514696533  0.427877290 -0.691209791  1.1214395016
##  [61,] -0.303937921  0.2195102429 -0.177772012 -0.966847954 -0.4534468747
##  [62,] -0.370589642  0.1881359754 -0.404935737  0.616217247  0.3213906647
##  [63,]  0.562045314  0.6087100581  0.546564854 -1.127522933  0.0423631652
##  [64,]  1.562104579  0.1679151372 -0.759164794  0.914358164  0.4221507490
##  [65,] -0.307419099  0.5669386920  0.323913746 -0.248765411  0.2401093667
##  [66,] -1.800555798  1.2416865299  0.546191663  0.025603755 -0.4886964204
##  [67,] -0.780803530  0.9680464791 -1.154511320 -0.234018960  0.2106001542
##  [68,]  0.243501794 -0.7449588229  0.901164989 -0.639258371  0.2572572643
##  [69,]  0.318511999  0.9865425504 -0.724604727  1.167513640 -0.3950871256
##  [70,] -0.155695975 -0.3662381423 -0.090378760 -0.082046491 -0.1027064113
##  [71,]  0.395563837 -0.6353653669 -1.046143203 -0.395446609  0.4200325778
##  [72,] -0.132154535 -0.2768798130  0.554030785  0.187167051 -0.2955056307
##  [73,]  0.118025861  0.2219809439  0.236114510 -0.198690863  0.0834334297
##  [74,] -0.140563287  0.1228052652  0.164854143  0.040425323 -0.2375809416
##  [75,]  0.089152229  0.0810432184  0.008917707 -0.013010484  0.1426505796
##  [76,]  0.252996727 -0.3221551566 -0.043456885 -0.401261618 -0.4983860014
##  [77,] -0.193686281  0.1925570034 -1.200835531  0.027174662  0.0545096490
##  [78,]  0.225428911 -0.5317507356 -0.751995565 -0.518521957  0.6561825798
##  [79,] -1.038563904  0.1303494327  1.505910954 -0.006619541 -0.3864339587
##  [80,] -0.999779797 -0.4491545309 -0.203159284  0.890661824 -0.0687494212
##  [81,]  0.736805720  0.0931148821 -0.548849539  0.929741566  0.1710456599
##  [82,]  0.331212303 -0.6604685218  0.483127310 -0.383953382  0.0299625586
##  [83,] -0.494038249 -0.1809526966 -0.693029162 -0.321202640  1.2130307510
##  [84,] -0.247720716 -1.9830952857 -0.064812692  0.673317030  0.2488693728
##  [85,]  0.293303760 -0.2526473413  0.760814035  0.442096802 -0.2483130580
##  [86,]  0.854198843 -1.0578870797  0.246599297  0.268291758  0.0528875299
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## [276,] -0.983023515 -0.1041939949  1.271501292 -0.181852971 -0.2020560780
## [277,] -0.801581787 -0.5012883274  1.399310331 -0.619467237  0.3217333923
## [278,]  0.235167642  0.0761654172 -0.868124389 -0.030755816  0.1837052038
## [279,]  0.259645931 -0.7659212831 -0.171331327 -0.771443767  0.2503776820
## [280,]  0.386626612  0.0020122656 -1.394599751  0.535355543 -0.6125133511
## [281,]  0.802480244 -0.1790725087 -0.588888791 -0.368026445 -0.1555218514
## [282,]  0.482401592  0.8485498995 -0.439878351  0.187371367 -0.9810781952
## [283,]  0.133037414  0.6534827324 -1.212225499  0.499259150 -0.6413672907
## [284,]  0.406502194  0.7165172399  0.480778116  0.925558289  0.1639291407
## [285,] -0.857974639 -0.6741941727  0.840754566 -0.600815722  0.2219338890
## [286,]  0.038978935 -0.7220043659  0.586611893  0.752720450 -0.5492553667
## [287,]  0.400500823 -0.3586637134 -0.511835579 -0.069931664  0.3513372646
## [288,]  0.822793804 -1.1842067114 -0.215174410 -0.208041555  0.5787408975
## [289,]  0.367378840  0.0070424388 -1.070586440  0.564778180 -0.6732674459
## [290,]  0.707731574  0.3200376804 -0.202871587  0.031149299 -0.5331046573
## [291,] -0.081437579  0.6813613159  0.423020726  0.339802365 -0.2840377311
## [292,] -0.448238235  0.5883060329  0.080163844 -0.336205536 -0.5854681151
## [293,]  1.782082642 -0.8786251058  0.424369024  0.453352217  0.1686013563
## [294,]  0.262999653  2.5161366718  0.184353081  1.516995025 -0.0388854969
## [295,] -1.028991209 -0.2410878726 -0.813808730 -0.445286831 -0.2550268203
## [296,] -0.767768447 -0.1184498761 -0.336592138  0.625874697  1.2319341578
## [297,]  0.424298678 -0.1658003787  0.354749610 -0.877756151  0.6822191559
## [298,] -0.583145614 -0.3361529386  0.012495691 -1.390367906 -0.1025393108
## [299,] -0.021967799 -0.5455360842 -0.094936125 -0.461983720  1.6215068235
## [300,]  1.938133198 -0.6013023488 -0.357609883 -1.101025575 -0.7146842916
## [301,] -0.568533563 -0.1138279703 -0.613242911 -0.355154778 -0.0453825308
## [302,]  0.737361526  0.1736037657 -0.361233504  0.692900730 -0.0526630204
## [303,] -0.126718864 -0.2544281997  0.408186660  0.192943852 -0.2835720653
## [304,] -0.061479981  0.4313114021  0.099934079 -0.890448988  0.4808252877
## [305,]  0.093734175 -1.8826517649  1.632717238  1.431294242 -0.4038404559
## [306,]  0.087368328 -0.0350587299 -0.772962725 -0.292136488  0.3733408245
## [307,] -0.674268055 -0.2830235204 -1.093907597 -0.326910311  0.1536629841
## [308,]  0.814679485 -0.1524666351  0.681117266  0.601996141  0.4859256479
## [309,]  1.875453301  0.5883067607  0.490080068  0.307284192 -1.0199760971
##                PC16         PC17
##   [1,] -0.204699168  0.399778790
##   [2,]  0.045288943  0.292915024
##   [3,] -0.271595154 -0.814045516
##   [4,] -0.371673537  1.078203419
##   [5,]  0.734034423  0.516096799
##   [6,]  0.370839736  0.464690533
##   [7,] -0.322143489  0.050306784
##   [8,]  0.531051672  0.194644777
##   [9,] -1.124665269 -0.473960208
##  [10,]  0.076492553  0.033336741
##  [11,] -0.534141622 -0.128982341
##  [12,]  0.084037407 -0.456830857
##  [13,]  0.189629446  0.456895464
##  [14,] -0.016716439 -0.021511422
##  [15,]  0.006422442 -0.329564249
##  [16,] -0.225723824 -0.788232416
##  [17,]  0.487690414 -0.355745563
##  [18,] -0.216253994  0.281111017
##  [19,] -0.357368372 -0.574817902
##  [20,] -0.121585264  0.153361961
##  [21,] -0.325279346  0.341539699
##  [22,] -0.249217026 -0.517074387
##  [23,] -0.474336582  0.001382573
##  [24,]  0.020601136 -0.029383874
##  [25,] -0.421748563 -0.176386698
##  [26,] -0.375057468  0.459319241
##  [27,]  0.157050749  1.283191589
##  [28,]  0.172160415 -1.177121386
##  [29,]  0.840632915  0.308201578
##  [30,]  0.546906491  0.990041317
##  [31,]  1.833637726  0.602301402
##  [32,]  0.899009190 -0.685671003
##  [33,]  0.778795299  0.192681525
##  [34,]  0.282663097  0.192190653
##  [35,] -0.281726780 -0.102251797
##  [36,]  0.404702630  0.315448071
##  [37,]  0.252701007 -0.080408534
##  [38,]  0.835870432 -0.173405499
##  [39,]  0.794453324 -0.901139864
##  [40,] -0.664108490 -0.302257112
##  [41,] -0.699334673 -0.772619337
##  [42,]  0.302214498  0.526431365
##  [43,]  0.215644055  0.008363015
##  [44,]  1.218170500 -0.374050417
##  [45,] -0.107189826  1.558186080
##  [46,] -0.014697978 -0.110994738
##  [47,] -0.314501834  1.085094010
##  [48,] -0.453323188  1.568209576
##  [49,]  0.371135730 -0.880906339
##  [50,]  0.038378647 -1.504845090
##  [51,] -0.190277899 -0.215343711
##  [52,]  0.571180847 -0.485102183
##  [53,] -0.795216391  0.307609636
##  [54,]  0.101171607 -0.457206584
##  [55,] -0.836682394  1.227393045
##  [56,] -0.761838666  0.044936466
##  [57,] -0.093377912  0.519556971
##  [58,] -0.085545972  0.334201010
##  [59,]  0.820792154  0.214839663
##  [60,]  0.108966172 -0.162975362
##  [61,] -0.542958636  1.037635542
##  [62,] -1.090814185 -0.173869707
##  [63,]  0.397950756  0.601928262
##  [64,] -0.286457614 -0.316048608
##  [65,]  1.423427877  0.100505316
##  [66,] -1.311470262 -0.340525215
##  [67,] -0.360979053  0.384060109
##  [68,]  0.046545960  0.364930671
##  [69,]  0.851869088  0.039331283
##  [70,]  0.125575693  0.027204718
##  [71,]  0.339668208  0.511883358
##  [72,]  0.135095885 -0.227962988
##  [73,] -0.161028009 -0.359990351
##  [74,] -0.151488592  0.364242693
##  [75,]  0.032547772 -0.019961277
##  [76,] -0.125258951 -0.040086038
##  [77,] -0.314385878 -0.543428311
##  [78,] -0.335717440  0.228175597
##  [79,]  0.400994735 -0.072763914
##  [80,] -0.528254127  0.151448992
##  [81,]  0.139513375  0.283297565
##  [82,] -0.005952746  0.259756203
##  [83,]  0.220449326  0.205910512
##  [84,]  0.821389639 -0.280463409
##  [85,] -0.616768168 -0.143967535
##  [86,]  0.587250538  0.095098054
##  [87,] -0.057818756 -0.333248457
##  [88,] -0.618241629  0.030801222
##  [89,]  0.262114853  0.284029297
##  [90,] -0.441595058  0.570186068
##  [91,]  0.546853402  0.247395413
##  [92,] -0.954452414 -0.237225566
##  [93,] -0.690367526  0.648356547
##  [94,]  1.196418062 -0.755162981
##  [95,] -1.025634831  0.626103061
##  [96,] -0.491732734 -0.231372581
##  [97,]  0.162249355  0.180426095
##  [98,]  0.601243917 -0.104024116
##  [99,] -1.217306954 -0.042251874
## [100,]  0.210795257 -0.266528766
## [101,]  0.009178791 -0.140306083
## [102,] -0.239832184 -0.505299089
## [103,] -0.001081145  0.061331010
## [104,]  0.225753874  0.024185581
## [105,] -0.423907862  0.044826848
## [106,] -0.049813183  0.066391359
## [107,]  0.144666199  0.249381777
## [108,]  0.288291683  0.147150980
## [109,]  0.683932546 -0.766405649
## [110,] -0.165238363  0.413606088
## [111,] -0.311500803  0.275308649
## [112,]  0.470357058  0.841243335
## [113,]  0.222169322 -1.078565979
## [114,] -0.168079224  0.872922772
## [115,]  0.877633521  1.155793976
## [116,]  0.248481964  0.515447773
## [117,] -0.215599949  0.058770936
## [118,]  0.514993586  0.210590031
## [119,] -0.226150793 -0.086942561
## [120,]  0.289380434  0.313280968
## [121,]  0.215127207 -0.235851294
## [122,]  0.018379895 -0.540713487
## [123,] -0.445011923 -1.187395940
## [124,] -0.197477228  0.266806473
## [125,] -0.289242777 -0.037798448
## [126,] -0.565139828 -0.738008042
## [127,] -0.159623044 -0.074763111
## [128,]  0.075685920  0.058279950
## [129,] -0.639909303  0.323712286
## [130,]  0.029766279  0.032157735
## [131,]  0.251431807  0.393080370
## [132,]  0.099890861 -0.888438144
## [133,]  0.278208194  0.028194637
## [134,] -0.035768643  0.342225755
## [135,] -0.465900314 -0.053961025
## [136,] -0.579918745 -0.349760333
## [137,]  0.000772863  0.151658109
## [138,]  0.209223668 -1.243826974
## [139,]  0.869070173  0.233877079
## [140,]  0.805399365  0.872283165
## [141,]  0.341425105  0.022592252
## [142,] -0.684397168 -0.936264140
## [143,]  0.869141848 -0.006288726
## [144,] -0.404210072 -0.522821842
## [145,]  0.676296036 -0.021386986
## [146,]  0.152334617 -0.236617040
## [147,]  0.100548266  0.546407053
## [148,] -0.614292886  0.646342147
## [149,]  0.157997524  0.030636773
## [150,] -0.396764299 -0.190573406
## [151,] -0.644069677 -0.846298375
## [152,]  0.284353292  0.503158969
## [153,]  0.173424869  0.019842343
## [154,]  0.044405912 -0.388242074
## [155,]  0.824834606  0.325438074
## [156,]  0.121962865 -0.861216712
## [157,] -0.442513188  0.702610115
## [158,]  0.793495320  0.334082201
## [159,]  0.447669504 -1.216843843
## [160,]  0.090886418 -1.371108370
## [161,] -0.438017503  0.002962693
## [162,]  0.541409695 -0.450589729
## [163,] -0.820401346  0.677621810
## [164,]  0.226252313 -0.216161914
## [165,] -0.677481397  1.415588471
## [166,] -0.583691233  0.119191040
## [167,]  0.293109180  0.174793193
## [168,] -0.203669862  0.239594626
## [169,]  0.743351273  0.219123542
## [170,]  0.130802257 -0.400058587
## [171,] -0.410579567  0.611738612
## [172,] -1.026212619 -0.272878294
## [173,]  0.242101208  0.488238862
## [174,] -0.288948646 -0.279987488
## [175,]  1.601354083 -0.114113845
## [176,] -1.520591312 -0.365248874
## [177,] -0.085103098  0.421068268
## [178,]  0.047903515  0.346408715
## [179,]  0.290577969  0.257721538
## [180,]  0.058594121 -0.016260362
## [181,]  0.351179366  0.395519794
## [182,]  0.067019098  0.018984832
## [183,]  0.069867765 -0.454941763
## [184,]  0.068081891  0.334040887
## [185,] -0.180412417  0.376233283
## [186,] -0.039127144  0.230944364
## [187,] -0.461598407 -0.299418857
## [188,] -0.863571623  0.415674312
## [189,]  0.164826381 -0.745791996
## [190,]  0.055938829 -0.226902271
## [191,] -1.130935409  0.447494847
## [192,] -0.780931794 -0.127862513
## [193,] -0.218573295 -0.492468351
## [194,] -0.164408869 -0.368908455
## [195,] -0.723395579  0.067538846
## [196,]  0.685196206  0.204171257
## [197,]  0.169355098 -0.549958598
## [198,] -0.769993878  0.122808536
## [199,]  0.128325234  0.614367708
## [200,] -0.115885447  0.264880595
## [201,]  0.569809145  0.268030342
## [202,] -1.012129894 -0.350160623
## [203,] -0.449618464  0.852052206
## [204,]  1.060227957 -0.534824136
## [205,] -0.614394865  0.846168128
## [206,] -0.773683331  0.063697140
## [207,]  0.510641502  0.044842721
## [208,]  0.539028601 -0.851370448
## [209,] -1.093386790 -0.122726928
## [210,] -0.155246654  0.001096426
## [211,] -0.194613598 -0.072297240
## [212,] -0.321072705 -0.504598778
## [213,]  0.179998006 -0.184224234
## [214,]  0.259444768  0.009943970
## [215,] -0.780618138  0.139516314
## [216,] -0.198320989  0.234820841
## [217,]  0.268641865  0.234126153
## [218,]  0.453731649 -0.077289733
## [219,]  1.088579218 -0.729502626
## [220,] -0.676442863  0.168806418
## [221,]  0.347355852 -1.056801166
## [222,] -0.165990170 -1.283069689
## [223,]  0.332638512 -0.293672149
## [224,]  0.795452124 -0.679781217
## [225,] -0.988260241  0.662611902
## [226,]  0.110787399 -0.291810588
## [227,] -0.252893278  0.923464117
## [228,] -0.433616613  0.144755671
## [229,]  0.066773967  0.275017663
## [230,]  0.063241523 -0.101200129
## [231,]  1.179012497  0.462607684
## [232,] -0.019352945 -0.148293626
## [233,] -0.615282088  0.926318797
## [234,] -0.681058673 -0.744278153
## [235,]  0.786713435  0.356755296
## [236,] -0.374744887 -0.315348333
## [237,]  1.269945960  0.064941224
## [238,] -1.574325649 -0.425168932
## [239,] -0.740202720  0.388446323
## [240,] -0.117226699 -0.428558305
## [241,]  0.955826543 -0.268608022
## [242,] -0.232986784  0.174246513
## [243,] -0.030911579 -0.178010067
## [244,] -1.116037385 -0.443587411
## [245,]  0.040368748  0.267750892
## [246,]  1.404264474 -1.478292614
## [247,]  0.978839680  0.483021714
## [248,]  0.603511293  1.157426119
## [249,]  0.692486224  0.040663628
## [250,] -0.722358199 -0.980492359
## [251,]  0.905558470  0.015177064
## [252,] -0.818092266 -0.133033980
## [253,]  0.321527445 -0.257408901
## [254,] -0.070998352  0.016638914
## [255,]  0.637360258  0.497985009
## [256,] -0.183950774  0.629102932
## [257,]  0.001359994 -0.002573657
## [258,] -0.199281757 -0.231513525
## [259,] -0.767591488 -0.674397629
## [260,]  0.473512663  0.278870895
## [261,]  0.279643315 -0.373044027
## [262,]  1.231233143 -0.616917441
## [263,]  1.196629303  0.206480172
## [264,]  0.154833871  0.622433628
## [265,] -0.106378218  0.206223917
## [266,]  0.516903811  0.396282048
## [267,] -1.619758037 -0.272082445
## [268,]  0.326323508 -0.089511243
## [269,] -0.174273385 -0.580481396
## [270,]  0.117172450 -0.841650045
## [271,]  0.058390380  0.788983893
## [272,]  0.062226434 -0.005549539
## [273,]  0.120922819 -0.511551264
## [274,] -0.104788706 -0.658045736
## [275,]  0.155305470 -0.417142635
## [276,]  0.258037515  0.001018338
## [277,] -0.471111047 -0.560894424
## [278,] -0.009003091  0.546602298
## [279,]  0.087872999  0.607421705
## [280,] -0.181710770 -0.644080424
## [281,] -0.184704565  0.404085944
## [282,]  0.381975583 -0.300021491
## [283,] -0.599984450 -0.026298504
## [284,] -0.130302106  0.170677295
## [285,] -0.054769022  0.159784347
## [286,] -0.357835410  0.115076387
## [287,] -0.335197519  0.362168104
## [288,]  0.068117172  0.532982330
## [289,] -0.109459288 -0.700975579
## [290,]  0.057996353  0.237331002
## [291,]  0.442745185 -0.109642684
## [292,] -0.638324403  0.131842402
## [293,] -0.586836031 -0.339105240
## [294,]  0.622801658 -0.405256743
## [295,]  0.146444590 -1.191554915
## [296,]  0.643560584  0.500112321
## [297,]  0.473122824  1.188323428
## [298,]  0.244203227  0.124670211
## [299,] -0.932773979 -0.723538859
## [300,]  0.720091571  0.108483530
## [301,] -0.501085666 -0.447556210
## [302,]  0.718340959 -0.098268391
## [303,]  0.109617474 -0.207952469
## [304,]  0.030515055  0.610897882
## [305,] -0.400852865  0.425130764
## [306,] -0.037178820  0.247090067
## [307,] -0.562633443 -0.019336438
## [308,] -0.714004235 -0.783153726
## [309,]  0.737576367  0.096973111
# Identifying the scores by their survival status
cancerp_pca <- cbind(data.frame(LUNG_CANCER),cancer_pca$x)
cancerp_pca
##     LUNG_CANCER          PC1          PC2         PC3          PC4          PC5
## 1             1 -0.646329947  0.332751806 -0.44274023  2.859184418  0.122598754
## 2             1 -0.610508061  0.058855781  0.83878638 -1.618262677 -1.600337930
## 3             0 -0.749550736 -1.504421159  2.66955055 -0.633003311 -0.554423032
## 4             0  1.096019632  2.420201554 -1.33296429 -0.623882219 -1.620199492
## 5             0  0.036188930 -1.476567174  1.06322075 -0.297399332  0.877535001
## 6             1 -0.532567242 -1.816704968  1.59490775  0.295408659  1.957759532
## 7             1 -2.543550172 -0.443750841  0.65879801 -0.490274648 -2.164652907
## 8             1  2.572207921 -0.611692066  0.98184227 -0.400242160 -2.014776748
## 9             0  1.272938608 -1.748902681 -2.03358144 -0.603715268 -0.190135930
## 10            1  1.396823254  2.844502270 -1.74624933 -0.548914628 -0.481234509
## 11            1  2.064989024 -1.179537297  0.77287410  1.619240317  0.200840281
## 12            1 -3.094017924 -0.236356800  0.18223710  0.351212010  1.270144781
## 13            0  0.217887666 -2.889346007 -0.91100600 -1.432307481 -1.045267875
## 14            1 -3.138457875 -0.373951998 -0.53082600  0.580383563 -1.106225675
## 15            0 -2.644849262  1.404467949 -1.44318316  0.143100628  0.232452899
## 16            1  1.650628200 -0.224745382  3.27395413 -0.093011818 -0.017887882
## 17            1 -2.832351242  0.682525475 -0.73821564 -0.010801951  0.679269335
## 18            1  1.926614145  2.783633537 -0.57374848 -1.250303351 -1.057854292
## 19            1  2.058726013 -1.588839942  1.68092889 -0.276981888 -0.505797399
## 20            0  0.277622753 -2.858606054 -0.42259847 -2.045803131  0.939549144
## 21            1  3.229605844 -1.107957864  0.54769701 -1.054795775 -1.494603821
## 22            1  1.856494117  1.281078425  1.72529424  0.500791276  1.185679005
## 23            0 -0.050480044 -3.127406007 -3.04980327 -1.990025288 -0.705699392
## 24            1 -3.114648178 -0.180587030  0.10426359  0.266726364 -1.323963055
## 25            1  0.277610744  3.357861077  0.49327829  0.917467589  0.437189391
## 26            1 -0.593103049  0.624184222  0.58814373  2.058674696 -0.508287510
## 27            1  0.798726715  0.817444755  0.93374653 -0.444838292 -2.523918618
## 28            0 -1.483179713 -1.292781315  1.00754634  0.715640195  0.065334512
## 29            1  1.135171580  0.783408309 -1.75430086  0.465724163 -0.417313447
## 30            0 -1.513992882 -1.471854090 -0.71445396  1.239531591  0.767188290
## 31            0  1.249804903 -1.966549418 -1.89456009 -0.936322757 -0.643651435
## 32            1 -1.015659657  1.565562602 -1.96636100  0.688684179 -1.044736566
## 33            0  1.959456710 -0.179323614 -1.66903462 -0.161407143 -1.632984057
## 34            1  2.332965976  0.401390187  0.14559217 -1.127745419 -1.393041621
## 35            0  1.785139801  1.845010472  0.27438022 -1.498888257 -1.437361903
## 36            1  2.803119610 -0.463091900 -0.61631147 -1.129814399 -0.672500165
## 37            1 -0.906183428 -0.252869061  0.60868898 -0.552044454  0.490794665
## 38            0  0.625607571 -1.096717211 -0.29615831 -1.482097111  1.247479925
## 39            1 -0.980782008 -0.452929695 -1.00809976 -1.791086031 -0.953341909
## 40            1 -2.531034433  1.054359249 -2.75170356  0.062941767  1.314619757
## 41            1 -1.849943675 -0.036969503 -0.70926167  0.528593229 -1.528261831
## 42            1 -0.768929068  0.787507023 -0.50866975  0.164717527  1.435220054
## 43            1  1.593703995  0.429036798  1.52983078 -0.546232596  1.925341348
## 44            1 -1.913272210  0.172794143  0.20744605 -0.721150606 -1.789307797
## 45            1  1.543800949  0.459571313 -1.73845136  0.640217881  2.124908844
## 46            1  0.292377930  1.094376928  0.98377124  1.985566661 -0.599839321
## 47            1 -0.251600030  0.717276148  0.11116195 -0.575662628 -0.910947467
## 48            1  0.254838293  0.616454646  0.11114292  1.765377472 -0.055649992
## 49            1  0.179367433  1.125141361  2.32349723 -0.520119821  0.277971205
## 50            0  0.952911843  1.162517658 -0.71030972 -2.443376329  1.135427261
## 51            1 -0.851848170  0.904980380  1.94819723 -2.525220801  0.637015235
## 52            1  0.301087025 -0.841444915 -0.33470279  0.020924532 -0.407424612
## 53            1 -0.906545994  1.108874215  1.03521271  0.179671277 -0.804835301
## 54            1 -1.669956979  0.706463198  0.54089194  0.336371630 -0.952496542
## 55            1  0.195017025 -0.473764877  0.02002028 -0.520758210  2.360776695
## 56            1  0.200650077  2.716951889  1.41770341 -0.952121471  0.740632192
## 57            1  0.518073225 -1.367268061  2.81032243 -0.783212228 -0.937364905
## 58            1 -1.831824121  1.109402015 -0.45190838 -0.415424258  1.192288451
## 59            1  0.685756178 -0.408794213  0.31395717  0.052650501 -0.299515433
## 60            1 -0.498748639  0.460812608  0.14593215  1.348117096 -1.331297016
## 61            1 -0.851501742  1.873535014  1.07688266  1.057769336  1.654911975
## 62            0  1.671406217 -0.423441611  0.01975544 -0.908557402  0.637102625
## 63            1 -1.102287719  0.573598828  1.07737079  0.769959205  1.589212310
## 64            1  0.487489582  1.589885359 -0.52386479 -1.031169208  2.329019058
## 65            1 -1.821523333  0.607204567  2.39323915  0.916516254  0.021873142
## 66            1  1.890194887  0.314196298  0.21915753  1.943292140  0.447955709
## 67            1 -0.908993115 -1.002601881  2.42194180 -0.792706294  0.098085784
## 68            1 -2.188253111 -1.295291142 -0.20414494  0.389988620 -0.418881441
## 69            1  1.922127515 -0.483661450 -0.89450174  1.892882896 -0.799898913
## 70            1  1.831473258 -1.208432390  0.77153641  2.788481409  0.126999960
## 71            1  1.111645609  2.745232439 -1.90160470  0.587416793 -0.459646651
## 72            1  1.972055116 -0.866834386  1.97362887  1.622670501 -1.020641169
## 73            1 -3.014541351  0.230927487  1.82358730 -0.870777134  0.323242135
## 74            1  0.297544932 -3.341535872 -2.66498436 -0.870757883  0.580788533
## 75            1 -3.123513629 -0.202316474  0.02439536  0.353201837 -1.241766589
## 76            1 -2.175119346  0.619405502 -1.87693522 -0.203685676  0.728913726
## 77            1  0.988165063  0.281111344  2.73257900  1.428695160  0.826564602
## 78            1 -3.171148404 -0.393624263 -0.52860137  0.462431181 -1.108134631
## 79            1  1.909872378  2.594516335 -1.37039805 -0.316273317 -0.384527514
## 80            1  1.884232732 -0.836929091  0.25971121  2.107873428 -1.134661282
## 81            0  0.148410514 -2.759622666  0.17058795 -2.012337053 -0.253735238
## 82            1  3.159260208 -1.376912455 -0.46218545 -0.031919056 -0.631448204
## 83            1  1.589202745  3.215922052  1.45544104 -1.156249670 -0.416540691
## 84            1 -0.735262114 -0.558683606  0.06426583 -0.614419304  3.046112719
## 85            1 -2.492696658 -0.248148077  0.57351965 -1.485832190 -0.156211037
## 86            1  0.164831585  1.067984585  0.76191427  0.778873264 -0.004490012
## 87            1 -0.791080564  1.277284906  0.13896203 -0.512508540  0.424119906
## 88            1  1.019972886  1.038546046  0.67879987  0.166896049 -1.036950670
## 89            1  1.355490521  1.048191345 -1.19753355 -1.835391137  0.487381401
## 90            1 -0.217694604  1.268039722  0.47349157 -1.166491895 -0.149140965
## 91            1  0.200980870  1.569364821  0.23589533 -1.010042731  0.739065292
## 92            1 -1.224091912 -1.370670443  1.95314352 -1.673818763  0.298939223
## 93            1 -1.377079915  1.986294419  0.87166613 -2.146700312 -1.490469516
## 94            1  1.105509567  1.009068862  0.89835083  0.952703555  1.771596512
## 95            1 -1.763739245  0.521690848  0.52910283 -1.278362192 -1.910301720
## 96            1  2.144246653  1.031814241  0.70297021 -0.327085070 -1.299959938
## 97            1 -0.247301899  0.219966733 -1.52379872  0.759730600 -0.649174503
## 98            1 -0.943580309 -0.985801589 -2.47162486  0.257887623  0.377111320
## 99            1  1.434728986  0.425244821  0.30490166  1.146598321  0.613218154
## 100           1 -3.084789560 -0.318539996 -0.37773171  0.447133452 -1.342039635
## 101           1 -2.211988131  0.291466382 -3.00610005  0.509360032  1.226245309
## 102           1  0.934186102  0.103006060  2.09662512  2.008597406  1.345721614
## 103           1 -3.134406710 -0.118005299  0.30107545  0.285470960 -1.220197353
## 104           1  1.829037095  2.049999607 -3.14856312  0.573307112  0.274730687
## 105           1  1.889637650 -0.929392727 -0.06656941  2.287498244 -1.058126770
## 106           1  0.304495611 -2.796890852 -0.22372072 -2.193562275  0.775896724
## 107           1  3.150251750 -1.266687571 -0.15055069  0.047749838 -0.490198468
## 108           1  1.504721972  2.576287720 -0.70174306  0.107804727  0.494154681
## 109           1 -0.513569276 -0.429919365  0.66685573 -2.146489489  1.272448570
## 110           1 -2.049787993 -0.595265518 -1.39788656 -1.626354625  0.259757990
## 111           1 -0.548863117  0.551657627  0.36348773  1.955891473 -0.754455175
## 112           1  0.137370850  1.157565543 -0.22654103  0.220013284 -2.581582640
## 113           1 -0.769133382 -1.651851800  2.04076114  0.144667909  0.027932525
## 114           1  1.052948611  1.877461485 -3.18476295  0.436016597 -0.942808927
## 115           1 -0.832893079 -1.520043078  1.23238975  0.789310913  1.071200271
## 116           1 -0.521560718 -1.774839073  1.77212639  0.062067842  1.766517195
## 117           1 -2.590558669 -0.606042808  0.07011790  0.065104794 -1.677476972
## 118           1  2.565856126 -0.636635561  0.90085819 -0.352743399 -1.971483866
## 119           1  1.890132650 -1.553285458 -0.21632974  2.489127348 -0.444483208
## 120           1  1.809485293  2.507239709  0.23379629 -0.904604737 -0.130106958
## 121           1  1.154753405 -0.820601807 -0.18191235  3.258811319 -0.010433839
## 122           1 -3.068643554 -0.358110282 -0.17957410  0.278724442  1.079820384
## 123           1  0.603092803 -1.663570228 -0.81847194 -1.742527977 -1.373236514
## 124           1 -0.262265717 -0.458918399  1.14583763  0.431171055  0.242487727
## 125           1 -2.166676433  1.025027556 -2.44144452 -0.175700086  0.158619707
## 126           1  1.396820173 -1.775823130  0.44315452  0.164190546  1.111925399
## 127           1 -2.621538470 -1.080128160 -1.50955976  0.829755886 -1.228986208
## 128           1  1.904628487  2.458422492 -1.72758409 -0.464085245 -0.547767196
## 129           1  2.449232521 -1.233115913  1.14940570  0.807738005 -1.464755784
## 130           0  0.346806820 -2.486510669  0.79296731 -2.700072211  0.411814347
## 131           1  3.029389183 -1.278867895  0.12853282  0.002537778 -1.822456522
## 132           1  1.929414827  1.312693320  1.78007480  0.409498610  0.912824308
## 133           1 -0.087138867 -2.322217437 -0.65856528 -1.925296028 -0.156916374
## 134           1 -3.286936885 -0.510578871 -1.06794608  1.550312925  0.014328320
## 135           1 -0.243063096  3.265766261  0.36303718  0.455074271 -0.101216908
## 136           1 -0.885383059 -0.103152291  0.79354384  1.149680047  0.191778725
## 137           1  0.779845934 -1.412199847 -1.48333758  0.232939883 -1.659993771
## 138           1 -1.475619881 -1.358995678  0.78667103  0.785254199  0.063938933
## 139           1  1.315156524  1.874152974  1.90819130 -1.745565666 -2.120481240
## 140           1 -1.435594309 -0.886655409  1.17170443  0.402456719  0.175080477
## 141           1  0.311554205 -1.503514600  1.98669876 -0.611745934 -0.377702324
## 142           1 -1.898169897 -0.689807691 -1.77090536  1.813131302 -0.926438974
## 143           1  1.817982682 -0.274894663 -0.25700981  0.816135845 -1.374023354
## 144           1  1.132188201  0.097406071  1.56257454  1.507813279 -0.597525384
## 145           1  1.041211639  2.476633973 -2.22422610  0.853838815  0.789743107
## 146           1  1.911956582 -1.279682355  0.58493540  2.442926394 -0.412810097
## 147           1 -2.208254898  0.244829063  1.39493556 -0.446948312 -0.084142771
## 148           1  0.199618587 -1.606668229 -0.56648477  0.211079060  1.819639955
## 149           1 -3.151824202 -0.105442765  0.28680901  0.530946496 -0.974148171
## 150           1 -2.581152399  1.660530129 -0.45658460 -0.913041511 -0.642489672
## 151           1 -1.821212050  0.049106818 -0.42528735  0.326193983 -1.727503000
## 152           1 -0.709027954  1.118219938  0.61257539 -0.562639222  0.859330817
## 153           1  1.527353442 -0.054701131 -0.07747901  0.328574008  2.559335815
## 154           0  0.134446169  0.264009802 -1.70348774 -1.428607876 -0.536373103
## 155           0  2.379419131 -0.094554298  0.55507534 -2.767771658  0.132335453
## 156           1  1.816004356  0.546117886 -3.21264766  0.454846344  0.862978356
## 157           0  0.693446059  0.977045613  0.26008812 -3.763916185 -2.021635959
## 158           0  1.637082331 -0.335000397 -2.05755169 -0.746108139 -0.416159349
## 159           1  0.296933463  1.194165867  2.60436670 -1.181630957 -0.546751798
## 160           0  0.822754284  0.670235764 -2.41335728 -1.103663683  2.312033587
## 161           1 -0.918911402  0.663806963  1.18690797 -2.128116926  1.024959096
## 162           1  0.231900961 -1.270641543 -1.76967126  0.862961366  0.236368161
## 163           1 -1.013939681  1.262821648  1.47304856  0.585206501 -0.098566521
## 164           1 -1.772694007  0.767271176  0.63712578  0.973149028 -0.128283972
## 165           1  0.113097963 -0.357041885  0.30262585 -0.029388012  3.038456413
## 166           1  0.075576812  2.276081375 -0.14913244  0.428758735  1.958389064
## 167           1  0.477358107 -2.002383447  0.60892730  0.553159679 -0.100163895
## 168           1 -1.789229364  1.010323518 -0.71414648 -0.663628669  0.826928708
## 169           1  0.719595969 -0.266957041  0.81937861 -0.376044152 -0.660229054
## 170           1 -0.479345237  0.029424455 -1.25225042  1.746517856 -1.293222426
## 171           1 -0.706487604  1.979788355  1.48164274  0.256635741  0.659195101
## 172           0  1.659264316 -0.669984273 -0.80889570 -0.497190062  0.868951875
## 173           1 -1.053631487  0.418816948  0.64807542  0.512000760  1.171296835
## 174           1  0.439619994  1.347267284 -1.34471999 -0.491319346  2.768031869
## 175           1 -1.736485551  0.889505297  3.31946123  0.301066951 -0.567055601
## 176           1  1.908193822  0.100984757 -0.40588659  1.869485714  0.234457926
## 177           1 -1.025193951 -1.347023632  1.14815308  0.528994073  1.290656942
## 178           1 -2.229264288 -1.622311063 -1.29643165  0.990124308  0.004899612
## 179           1  1.957225328 -0.433792361 -0.55469125  1.069085426 -1.511190662
## 180           1  1.838526733 -1.356872831  0.31115872  2.847776221  0.079447061
## 181           1  1.180112751  2.940457687 -1.22406253 -0.005852669 -1.024121550
## 182           1  1.811861750 -1.441142807  0.01690577  3.101211177  0.312426585
## 183           1 -3.110670459 -0.364952154 -0.24358794  0.575227017  1.429197339
## 184           0  0.360229263 -2.696506149 -0.58357746 -1.726264724  0.050562343
## 185           1 -3.223541067 -0.179218190  0.09257126  0.673772079 -0.685860956
## 186           1 -2.269746579  0.759892939 -1.50517585  0.258232091  1.433596248
## 187           1  2.747577269 -0.892695063  0.37334010 -0.956311448  1.532003894
## 188           1 -0.149697264 -1.642331214 -2.28814301 -1.471419303 -0.781235965
## 189           1  2.400777592  0.347128955 -1.71026348 -1.021489585  0.434261725
## 190           1  2.664155409 -1.393549647 -1.71837991  0.529051941  0.057805594
## 191           1  0.613534144 -1.458382780  0.89659577 -3.179203564  1.045150296
## 192           1  2.833005133 -1.403952109 -1.83872171 -0.412027674  0.480801518
## 193           1  3.117056920 -0.179410694 -1.10177848 -1.856855416  0.106854315
## 194           1  1.396552964 -0.642255545  0.02050933 -3.110585372  1.836705087
## 195           1 -2.512642306  0.003850388  1.41044718 -1.765460899 -0.188561541
## 196           1  0.041302770  0.619388750 -0.80700898  2.078283851  1.142567875
## 197           1 -0.813244847  0.880928753 -1.22887662  0.288977960  0.912007999
## 198           1  0.986709032  0.840164793  0.05264538  0.423153898 -0.837258657
## 199           1  1.252252204  0.988451934 -1.42301728 -1.323117294  1.159512551
## 200           1 -0.137885258  1.481731866  1.13219939 -1.525196202 -0.559153131
## 201           1  0.136542296  1.207505130 -0.99116369 -0.216929658  1.363785406
## 202           1 -1.270419897 -2.048452421 -0.26872446 -0.709046147  0.847964695
## 203           1 -1.511779573  1.885698680  0.38947345 -1.030942437 -0.282150752
## 204           1  1.085397022  1.243127916  1.68487628  0.664169343  1.724253118
## 205           1 -1.937338444  0.418609362 -0.03359575  0.232284332 -0.284578291
## 206           1  2.079880884  0.956433882  0.49279972 -0.166467991 -1.020841607
## 207           1 -0.238660237  0.398472349 -1.03260961  0.864147837 -0.508793937
## 208           0 -0.159651843 -1.132594137 -0.05598138 -1.013129749 -0.784261739
## 209           1  1.500566250  0.840189583  1.66536450  0.435082161  0.072426854
## 210           1 -3.014209221  0.355964728  1.96591223 -1.080854377 -2.396209206
## 211           1 -2.105058072  0.929924423 -0.80062808 -1.017803085  0.046453380
## 212           1  0.942418911  0.054526904  1.96648773  1.934291974  1.240767541
## 213           1 -3.148924082 -0.594610120 -1.31041545  1.087399067 -0.793683557
## 214           1  1.878394695  2.398574133 -1.99024350 -0.062447648 -0.190863682
## 215           1  1.966715740 -0.630957885  1.05402026  1.155588169 -2.010604775
## 216           0  0.277041266 -2.759604202 -0.07945444 -2.231880620  0.846800791
## 217           1  3.171498795 -0.995402267  0.71278740 -0.251134699 -0.651266456
## 218           1  1.556928786  2.591469129 -0.66355483 -0.035006615  0.235938143
## 219           1 -0.616500433 -0.513737474  0.21506585 -1.061891800  2.369939157
## 220           1 -2.586211894 -0.187369377  0.72652260 -1.088595931  0.457090666
## 221           1  0.137716815  0.366509534 -0.16792988  0.543739987  0.849702117
## 222           0  0.865093182  0.844185218 -1.74842823 -1.798595288  1.737694179
## 223           1 -0.913971012  0.969266395  1.97298215 -1.716775781  1.472684147
## 224           1  0.313977949 -0.945041768 -0.72531396  0.292773295 -0.288118442
## 225           1 -1.072776501  0.599121897 -0.68085976  1.492600012  0.450812463
## 226           1 -1.699472023  0.930082069  1.24714633  0.260609994 -0.813935347
## 227           1  0.251825578 -0.075337937  1.19428496 -0.695732642  2.249570554
## 228           1  0.014567830  2.117497330 -0.74689429  1.102971967  2.580198736
## 229           1  0.504752774 -1.860630264  1.15079860  0.009577708 -0.529532914
## 230           1 -1.698692239  1.131623356 -0.33312414 -1.038468810  0.327760281
## 231           1  0.558690456 -0.191830970  0.83866091  0.887454211  0.824592143
## 232           1 -0.464475998  0.564705610  0.54205784  0.907998903 -1.720403026
## 233           1 -0.736607022  2.290777684  2.53098650 -0.131746814  0.602622034
## 234           1  1.791907070 -0.482831255 -0.20730594 -1.103593125  0.098407869
## 235           1 -1.021622690  1.026768352  2.49920628  0.201024453  1.131623848
## 236           1  0.511871527  1.643341139 -0.30949731 -1.318210021  2.062253193
## 237           1 -1.857682768  0.067118102  0.65282615  1.571807247  0.370261802
## 238           1  1.973432877  0.329461293  0.39577264  1.190688519 -0.369711578
## 239           1 -0.844025398 -1.043350556  2.43615654 -1.497678287 -0.655538378
## 240           1  1.798603632  1.277822318  1.64041006  0.964305961  1.712072698
## 241           1  0.567970913 -1.465901428 -1.40821954 -1.475588124  1.328585265
## 242           1 -3.128591618 -0.100406746  0.42598650 -0.002631206 -1.449540091
## 243           1  0.921300172  2.566347959  0.08444693 -0.327261230 -0.277565465
## 244           1 -0.707766669 -0.140351712  0.50896513  0.494931879  0.794661098
## 245           1  0.727027732 -1.433071548 -1.59685113  0.593875654 -1.235796634
## 246           0 -0.813209418 -1.199505257  0.40464481 -0.405256608 -0.735537650
## 247           1  1.137562086  1.419593842  0.28112686 -0.123186538 -0.567331492
## 248           1 -1.568549443 -1.353854798 -0.38152350  1.471266594  1.164907662
## 249           1  0.206337661 -1.720761209  1.11360977  0.581416058  0.745153770
## 250           0  0.582400965 -1.654341741 -4.03720871  0.592072897  0.127026158
## 251           1  1.852485410  0.064395647  0.86057895  0.277190722 -1.725563610
## 252           1  1.069824793  0.099379354  1.64192217  1.436102237 -0.464752520
## 253           1  1.320083419  3.019301770 -0.60379759 -0.838972788  0.575723760
## 254           1  1.826416008 -1.528447714 -0.21991298  2.977344774  0.131843922
## 255           1 -2.295131492  0.231836563  1.14798587  0.601866665  0.972169398
## 256           1  0.184324517 -1.188753076  0.66614989  0.264048756  2.108122913
## 257           1 -3.143108851 -0.334761125 -0.41121557  0.580820285 -1.073009725
## 258           1 -2.658851944  1.282851605 -1.79186198  0.149784893  0.220653288
## 259           1 -1.871308247 -0.027948405 -0.67512508  0.569331753 -1.428769300
## 260           1 -0.711591973  0.787827363 -0.51712533  0.015709149  1.149714717
## 261           1  1.686997211  0.200537154  0.82927435 -0.749102450  1.380292709
## 262           1 -1.858110215 -0.038377392 -0.44768335 -0.780682656 -2.102146836
## 263           0 -0.009983675 -1.961070989 -0.67218900  0.977524185  1.756913624
## 264           1 -0.640492349 -2.449177339 -0.47626302  1.394993461  2.816254162
## 265           1 -2.667743902 -0.624537600 -0.07078989  0.631216256 -1.022190383
## 266           1  2.455060778 -0.932060495 -0.13446506  0.605103847 -1.049802875
## 267           0  1.289042304 -1.784059560 -2.00134352 -1.157706179 -0.679250082
## 268           1  1.464834078  3.334018842 -0.17613207 -1.228668742 -0.968154666
## 269           1  2.198079582 -0.920094403  1.60613778  0.943922005 -0.588805903
## 270           1 -2.876746306  0.339743512  2.19185099 -1.486040419 -0.507401063
## 271           0  0.060055521 -3.317302160 -2.37218122 -0.195895671  0.166259201
## 272           1 -3.142504794 -0.257942521 -0.17738398  0.552812520 -1.059087544
## 273           0 -2.634807935  1.168554355 -2.23638980  0.468363114  0.337151628
## 274           1  1.505301199 -0.740318106  1.46628345  1.427782791  1.331421460
## 275           1 -2.740709424  0.722367627 -0.45692349 -0.908981952 -0.263057377
## 276           1  1.905774831  2.562920015 -1.43666755 -0.402881750 -0.453816513
## 277           1  2.017633169 -1.986659604  0.38967132  0.286357120 -0.144177349
## 278           0  0.099735552 -2.950607582 -0.86988372 -0.826878661  2.360250992
## 279           1  3.015656624 -1.371646389 -0.56504871  0.865577325  0.487728246
## 280           1  1.825438683  0.837995677  0.24336244  1.242694873  1.631988024
## 281           0 -0.131569292 -2.296085695 -0.47529079 -2.174913004 -0.202269462
## 282           0 -1.322834911 -1.037008743 -0.41131805 -1.699174863 -2.575108219
## 283           0  1.736775731  1.283284999 -1.49919175 -0.917952163 -1.119800076
## 284           1 -0.592930367  0.224645288 -0.78024226  2.755903856 -0.168581495
## 285           1  1.928894090  2.708029329 -0.86288820 -1.014020749 -0.920456081
## 286           1  2.367428208 -1.947699135 -1.30903111  2.358687696 -0.378804689
## 287           0  0.290098251 -2.530916123  0.71152818 -2.701725928  0.558829150
## 288           1  3.070879292 -0.884056499  1.49195594 -0.861410776 -2.416739566
## 289           1  1.901858849  1.316866466  1.83316729  0.347207053  0.949670177
## 290           1 -0.148458186 -2.510569491 -1.25163372 -1.591987828  0.190570397
## 291           1 -3.160670480 -0.142895407  0.08071687  0.912125001 -0.674116273
## 292           1 -0.350752444  2.762553158 -1.29900566  1.452158009  0.740670485
## 293           1 -0.898366238 -0.174979956  0.55300720  1.296536856  0.308268936
## 294           1  0.861502720 -1.425901982 -1.64547390  0.420718507 -1.767384879
## 295           1 -1.473211209 -1.294127913  1.01677328  0.634936076 -0.026911060
## 296           1  1.111453285  0.841309250 -1.52709178  0.333852745 -0.419205639
## 297           1 -1.529405423 -1.178528936  0.25100317  0.921255092  0.711687244
## 298           1  0.258107397 -1.743891382  1.19553857 -0.139263124  0.027543069
## 299           1 -1.904656129 -0.528637935 -1.18196439  1.415971336 -1.132951811
## 300           1  1.848956846  0.029663156  0.79616089  0.147726816 -1.830864913
## 301           1  1.150509115  0.284559833  2.21074344  1.095715426 -0.877160551
## 302           1  1.152918867  3.108695777 -0.10406543 -0.443281716 -0.231421332
## 303           1  1.932277477 -1.124180447  1.11643983  2.110205036 -0.653007261
## 304           1 -2.222289178  0.217516381  1.31604101 -0.408380875 -0.025831892
## 305           1  0.309135098 -1.125563191  1.01347625 -0.729745122  1.004636281
## 306           1 -3.290318919 -0.773981843 -1.92760392  1.864300336  0.137285445
## 307           1 -2.664442991  1.297484746 -1.64793851 -0.204320402 -0.026482672
## 308           1 -1.831829290  0.042083823 -0.43588975  0.322802182 -1.701712188
## 309           1 -0.648431973  1.114788359  0.51649880 -0.439377745  0.770588458
##               PC6           PC7          PC8          PC9          PC10
## 1    0.7182594090  0.0900371245  1.051744451 -1.937650817  0.4989633841
## 2   -0.6772550951  1.9777064114 -1.557168739 -1.216866754 -0.5305604825
## 3    1.1916488129 -1.2195053227 -0.411285727 -0.323523971 -0.1148162874
## 4    1.7403584683  0.6091639642  0.258612735 -0.654105790 -0.2130147794
## 5    2.1847893962  0.2198466952  1.845426766  0.627204075 -0.6014890431
## 6   -0.2480383908  1.4550678660  0.483870124  0.558138013 -0.2014692509
## 7    0.9965416546 -0.8530147261  0.684045214 -0.285018564 -0.7811912336
## 8   -0.5055130553 -0.4251606584 -0.227317424  1.333349131  0.1917601304
## 9    1.1709683751  0.1970313925 -1.162926497  0.312410711 -1.0231229714
## 10  -1.4206369931 -0.3235588013  0.045516341  0.241215288  1.0354175725
## 11  -0.9877439635 -0.2335341620  0.675723070 -0.141706192 -1.1092713774
## 12  -0.7610221388  0.7783351846 -0.103927236 -0.972945187  0.3836599781
## 13   0.7356356660 -0.1182467785 -0.538078442  0.115259335 -0.8498243779
## 14  -0.3303380494 -0.4144204301  0.078712304  0.509575391 -0.1786395470
## 15   0.8668959754  0.1542886143 -0.441232526  1.201097550 -0.7763798784
## 16  -1.0582597188 -0.7242179155  1.600738198  0.810017235  0.0978269150
## 17  -0.5049244711  1.7816022095 -0.061502145  0.001210227 -0.9101287848
## 18   0.1840838476 -0.0442652608 -0.003095435 -0.819714203  0.2257921571
## 19   0.4184360878  1.5182832851 -0.362960279  0.678886989 -0.0700320345
## 20  -0.1026575213  0.1029842000  0.139143879 -1.173656688  0.0186207447
## 21  -1.1480175988 -0.8296570774  0.839375250 -0.234943802 -0.0825857254
## 22   1.3263081293 -0.4222197926  0.444424752  1.718445639 -0.4170879515
## 23  -3.4638911787 -2.6363622952  2.172674109  1.263816491  0.8334590948
## 24  -0.0004180954 -0.1158383494 -0.076506354  0.541266927 -0.3670905070
## 25  -0.2750442777  0.9287661421 -0.325823814  0.423680522 -0.5182746874
## 26   1.0816548676  0.0640144973  1.274308400 -1.764172546  0.3344585771
## 27  -0.2832546918  1.2360719838 -0.187090224  0.315365054 -0.0554968227
## 28   1.3433206731 -0.8591849926 -0.936163793 -1.220062630  0.4830794498
## 29  -1.6799924024 -0.0281633721  2.156630368 -1.020784884 -1.1447949606
## 30   1.0710626285 -1.3284110672  1.834728862 -0.381994526  0.6811806747
## 31   0.8185042829  0.1595997123  0.965113863  0.982824838 -0.1867421466
## 32  -0.5116245789  0.2213173362  0.411993823 -0.538385421 -1.0926900877
## 33   1.2290071541  0.4714686091  1.461225803 -0.325889829 -0.2473663898
## 34  -0.0646666045  2.2433620737  0.710404490 -0.950511191 -0.7809675133
## 35   2.4754853111  0.2893439181  0.923999043 -0.982576123  0.6579637222
## 36  -0.1422025234  1.3713987956  1.491799348 -0.266482715 -1.0176272530
## 37   0.8160953361  0.5636397794  2.230793234 -1.029467745  0.4891853321
## 38  -0.3534221454 -0.7417774978  1.638132555 -1.319142919 -1.6484147935
## 39  -0.1721706898  0.0335387929  1.024852681 -1.148675650 -1.2064988678
## 40  -1.1755253233 -0.3055779800  0.531840085  0.641114542 -0.3585174104
## 41   0.3339185093  1.5334741172 -0.742220999  0.397824082  0.6322714144
## 42   0.1743686979 -2.4061791305 -1.430371076 -0.412504818 -0.2390151804
## 43   1.0164937988  0.2833156337 -0.990443898 -0.608638156 -0.8755992881
## 44  -0.6089020677 -1.6271801419 -0.979063296  0.261435435 -0.0709340761
## 45  -0.2960954667 -0.0609937498 -0.506122202  0.560648901 -0.3045133671
## 46  -0.4779798997  0.7123433988 -0.252310393 -1.474850571 -0.4690179776
## 47  -0.5681313101  1.8002197935  0.989506417  0.151660074  0.5940115661
## 48   0.0650024003 -1.6861801155 -0.882564748  0.225197238 -0.6288864935
## 49  -1.3100505736  0.3797064291 -1.171015537 -1.344665437 -0.7421368508
## 50   1.3420468766 -0.3811321637 -0.227571574 -0.652518402  0.3433578516
## 51  -0.8400332772 -1.4635314100 -1.078142846  0.099897456 -0.1895171928
## 52  -0.8236403909  1.1294305256  0.840477295  0.190213575 -0.6073655522
## 53  -0.7293181061 -2.1049759827 -1.159698724  1.358785707 -0.9020524475
## 54  -2.3456226474 -1.5198752771  0.052128540 -0.129470207 -0.1026399486
## 55  -0.8361005036 -0.9337361769 -0.234221327  1.426062323  1.7765311821
## 56   0.6763606802  0.0390138240  2.563417845  0.722616967 -0.3790244685
## 57   1.6946080427  0.0698616819 -0.534759032  0.043136450  1.5033693120
## 58  -0.3582806110  1.6811886957  0.042283265 -1.182450667  0.7849571961
## 59  -1.3495183401 -2.2578695319  1.090262317 -2.250237313  1.0030432414
## 60   0.2690629341  1.1554971565 -1.160881822  0.832217716  1.6653117813
## 61  -0.7234518984 -0.6127871702 -0.742339680 -0.649836684  0.8693699595
## 62   2.7376481997  0.5069278238  1.443017228  1.237888114  0.4514609616
## 63   1.4658335990 -0.9257069648 -0.898460096  1.182587630  0.7225827545
## 64  -0.3455726719  0.3440809009  0.421923404 -0.198799051 -1.7624832578
## 65   1.0291862289  0.3015066007 -0.973691647  0.197857462  1.1499283042
## 66  -0.8641232698 -0.0765569415 -0.652176582 -0.405376799 -0.8177445459
## 67  -0.8224879637  0.4260268121  1.467835590  0.414959404  0.5598897961
## 68   1.4683182389 -0.1736121977  0.029019490 -0.125692739 -1.4472406140
## 69  -1.1647333718  1.0018628504 -2.021014782  0.026036013  0.7065863902
## 70   0.7122713714  0.4831732842 -0.770951147  0.048311261 -1.3917275625
## 71   0.2163691129  0.2332136225 -1.264055897  0.342708666  0.8105451156
## 72   0.8927285143 -0.0892148898 -0.031393992  0.512702951 -1.4173886846
## 73  -0.1471944405  0.8343504360  0.160820099 -0.725256307  0.0941240714
## 74  -1.2948417212 -0.0557786798 -0.137358569 -0.634600071 -0.5015041758
## 75  -0.0085485247 -0.0638697694 -0.138921766  0.508917015 -0.3690218531
## 76   0.8865859209 -0.8394523284  0.524187877  1.924133725 -1.0392422670
## 77  -0.9823598934  1.2710772242 -0.440050417 -0.551349005  0.2165906641
## 78  -0.3369973922 -0.5403419775  0.209784606  0.463483093 -0.1534376132
## 79   0.0259121267  0.4476842656 -0.627700825 -0.986909443  0.2319467291
## 80   0.2603971391  0.8509880060 -1.147268964 -0.332077475  0.4277897576
## 81   1.3454849598 -0.4571683277 -0.020774310 -0.503014456  0.0002491504
## 82  -1.3530858031 -0.3732312052  0.223143075 -0.520275980 -0.0422490303
## 83  -0.7627017522  0.3161724869 -0.237643091  0.721497336 -1.3314564476
## 84  -0.0620643948  1.6063796501 -1.349044882  0.595672201  0.4284075233
## 85  -0.6206514250  0.4762684616  0.434017829 -0.448693689  1.6330839047
## 86   2.1908847748  0.1637682633  2.454547104 -0.535495194 -0.5434528668
## 87   0.2751173563  2.4020282519  1.387369642 -0.084458879  1.8146097334
## 88   1.6504616104 -0.6662903002  0.575775492 -1.644130385 -0.1523657271
## 89  -0.2146076649  1.4666407787  0.505539732  1.817924110 -0.4343689651
## 90  -2.1768553940 -1.7351397721 -1.333156393  0.080157982 -1.2516603384
## 91   1.0186361905 -2.0232826855 -0.799342765 -0.912119506 -1.0274541464
## 92  -0.2200662088  1.8899057953 -0.629502096 -0.091212678  0.6710501797
## 93  -1.0107223981 -0.8968021944 -0.126530551 -0.421850393 -1.4183187612
## 94  -1.1577149024 -0.0636793450  1.564665414  0.807153497 -0.0043867516
## 95  -1.5072647311  0.0592587589  0.582670492 -0.164119150  0.3775130916
## 96   1.5259187055 -0.9655011371 -0.748051421 -1.302623761  1.4527806508
## 97  -0.1637854681  1.5368529740  0.950410816  1.721597416  0.9008138964
## 98   0.9508989263 -0.8494160616 -0.248636294  0.471625838  0.4169054384
## 99   1.0144025218 -0.4992410790 -0.560620283  0.691692676  1.7044333766
## 100 -0.3562594091 -0.5342511547  0.203608313  0.652327066 -0.1601264925
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## 304 -0.8242134745 -0.2005517233  1.866263998 -0.162230166  1.2491918924
## 305 -0.5806708637 -1.0993056715 -0.071064434 -0.836025698  0.2882833788
## 306 -0.5943934264  0.1107253930 -0.653395882  0.019173765 -0.1081640853
## 307  0.5500102538 -0.6588696646  0.287068731  1.294093947 -0.5254052273
## 308  0.4272639574  1.5292324864 -0.687199135  0.451762489  0.5889517563
## 309  0.5268382605 -2.2511204799 -1.404420153 -0.130277486 -0.4341384337
##             PC11          PC12         PC13         PC14          PC15
## 1    0.420523565  0.4334820544  0.016896184  0.568431041  0.4383575733
## 2    0.462308125  0.3986804449 -0.218844308  0.061830934 -2.0687208915
## 3   -1.315721292 -0.6118901582 -1.234182675  0.374500028  0.7773050725
## 4   -0.036031283 -0.2638657935 -0.338447239  0.010300783  0.5421504516
## 5   -0.912182701 -0.4352120930 -1.415924824  0.029107293  0.2282780957
## 6    0.006675664  1.2983623838 -0.206751142 -0.234096001 -0.6232337130
## 7   -0.681612182 -0.4367979407  0.627895778 -0.126860747  0.5778337358
## 8    1.570297126 -0.3494589711 -0.224076737  0.307935702 -0.1791024816
## 9    0.588029356  1.3889527245  0.379929206  0.698899496  0.2331253689
## 10   0.013843135 -0.3935900740  0.183078896 -0.531951622 -0.0795574606
## 11  -0.393455043 -0.8581065623  0.256269265 -0.857916040  0.0129291768
## 12   0.012211427  0.7468853985  0.391100484  0.158685593 -0.2626260427
## 13   0.249502857  0.0929055090 -0.044637030  0.616334219 -0.0808919597
## 14   0.108202924  0.0621200579 -0.074766804 -0.009759719  0.1656639689
## 15  -0.894184802  0.6667391909 -0.134044309  0.395128230 -0.5965953711
## 16   0.908454725 -0.2179462237  0.185976081 -0.004498742 -0.4711337983
## 17  -0.992433913 -0.7479697500 -0.485089739 -0.584556336 -0.1028938720
## 18  -0.796874258 -0.9948424816  0.538850685 -0.867448372  0.4749865902
## 19  -0.844001807 -0.4463708756  1.628548810 -0.604924292  0.2536040792
## 20   0.320441162  0.1598941284 -0.096108696  0.385799068 -0.0495534724
## 21   0.467789803 -1.2219438435  0.249408139 -0.731181079  0.4061416274
## 22   0.411759401 -0.2953011717 -1.528031755  0.251766287 -0.3967280920
## 23   0.951863976 -0.0769681900 -0.219517073  0.120893372 -0.3421600285
## 24   0.095539826  0.0651550583  0.029651045 -0.012197733  0.1471579650
## 25  -0.734840381 -0.7561054781 -0.278001541 -1.273542765  0.0662511665
## 26   0.494253801  0.0829017276 -0.087042222  0.335995178  0.6686192208
## 27   1.219675724  0.3473208400 -0.118633159  1.409979591  1.0286389588
## 28  -1.041488146 -0.2161509584 -0.829347522 -0.448322267 -0.2646588750
## 29  -0.837946225  0.2926483701  0.133017998  1.000956763  0.8888048793
## 30   0.404992386  0.1465291483  0.689510060 -0.526647777  0.4152453066
## 31  -0.863377283  0.8313440043  0.490013777  1.143399608 -0.8880189012
## 32   1.135636716 -0.4148927197 -1.304990553  0.638676216  0.2022641052
## 33   0.828808911 -0.6314252501 -0.319879928 -0.179981187 -0.9960511402
## 34  -1.045951865  0.0668733975 -0.398041733  0.851525389 -0.2799188786
## 35   0.009148572  0.9825179146 -0.693330830  0.687387035 -0.9228988259
## 36   0.003684991 -0.4452323697  0.131529168  0.435770915 -0.5539587221
## 37  -1.864892347 -0.2768934238 -1.318510710 -1.321186730 -0.2473171349
## 38  -0.021480573 -0.3037972350 -0.919328509  1.015139336 -1.1288114460
## 39  -1.480099028  0.0080071951 -0.864049795 -0.975689884 -0.4962413909
## 40  -1.149182018  0.1416856598 -0.300607468 -0.552503014 -0.3531137163
## 41   0.806124346 -0.1179494334  0.638998799  0.611840391  0.4739033034
## 42   2.023023934 -0.1990796775 -0.721549002 -0.445591628 -0.3057797375
## 43   0.118601406  1.1488752332  1.127125769 -0.819164504  2.0210436648
## 44   0.370000163 -0.3286131012 -0.391529217 -0.756123983  0.9131450099
## 45  -1.614973464 -1.2134306509  1.337189896  0.479254455 -0.7940825244
## 46  -0.822660699 -0.5381476425  1.351054267 -0.871938739  0.2867008044
## 47  -0.825820015 -1.4698517789 -1.565778171 -0.912485003 -1.6294596013
## 48  -1.665852215  0.3708029720  0.525802391  0.726885898  0.2313883640
## 49   1.008512627 -0.1394632519 -0.443699967  0.933724085  1.2044084929
## 50   0.400890266 -0.8467778863  1.276292343 -0.515240987  0.6590492803
## 51  -0.203704842  0.7304241801 -0.305652649  0.014290211  1.4018728347
## 52   1.318968269  1.2676593358 -0.089367897 -2.200932157 -0.0105380974
## 53  -0.471740318  0.0747768687  0.312992783  1.462436004 -0.3283840429
## 54  -0.248509625 -0.7626119578  1.151848027  0.102037854 -1.1656168492
## 55   0.059631997 -0.3422837836  0.631467132 -0.430910715  0.7213219035
## 56   1.187959690 -0.3529930654  0.325920926 -0.635921694 -0.3963700610
## 57  -1.516700646 -0.5463492685 -0.689798999  0.290699987  0.6539578856
## 58   0.063045575 -1.5632941214 -0.689317295  0.965257941 -1.1668081449
## 59  -0.585555242  0.3180404088 -0.613800091 -1.021079901 -0.7911169580
## 60   0.168377749 -0.6514696533  0.427877290 -0.691209791  1.1214395016
## 61  -0.303937921  0.2195102429 -0.177772012 -0.966847954 -0.4534468747
## 62  -0.370589642  0.1881359754 -0.404935737  0.616217247  0.3213906647
## 63   0.562045314  0.6087100581  0.546564854 -1.127522933  0.0423631652
## 64   1.562104579  0.1679151372 -0.759164794  0.914358164  0.4221507490
## 65  -0.307419099  0.5669386920  0.323913746 -0.248765411  0.2401093667
## 66  -1.800555798  1.2416865299  0.546191663  0.025603755 -0.4886964204
## 67  -0.780803530  0.9680464791 -1.154511320 -0.234018960  0.2106001542
## 68   0.243501794 -0.7449588229  0.901164989 -0.639258371  0.2572572643
## 69   0.318511999  0.9865425504 -0.724604727  1.167513640 -0.3950871256
## 70  -0.155695975 -0.3662381423 -0.090378760 -0.082046491 -0.1027064113
## 71   0.395563837 -0.6353653669 -1.046143203 -0.395446609  0.4200325778
## 72  -0.132154535 -0.2768798130  0.554030785  0.187167051 -0.2955056307
## 73   0.118025861  0.2219809439  0.236114510 -0.198690863  0.0834334297
## 74  -0.140563287  0.1228052652  0.164854143  0.040425323 -0.2375809416
## 75   0.089152229  0.0810432184  0.008917707 -0.013010484  0.1426505796
## 76   0.252996727 -0.3221551566 -0.043456885 -0.401261618 -0.4983860014
## 77  -0.193686281  0.1925570034 -1.200835531  0.027174662  0.0545096490
## 78   0.225428911 -0.5317507356 -0.751995565 -0.518521957  0.6561825798
## 79  -1.038563904  0.1303494327  1.505910954 -0.006619541 -0.3864339587
## 80  -0.999779797 -0.4491545309 -0.203159284  0.890661824 -0.0687494212
## 81   0.736805720  0.0931148821 -0.548849539  0.929741566  0.1710456599
## 82   0.331212303 -0.6604685218  0.483127310 -0.383953382  0.0299625586
## 83  -0.494038249 -0.1809526966 -0.693029162 -0.321202640  1.2130307510
## 84  -0.247720716 -1.9830952857 -0.064812692  0.673317030  0.2488693728
## 85   0.293303760 -0.2526473413  0.760814035  0.442096802 -0.2483130580
## 86   0.854198843 -1.0578870797  0.246599297  0.268291758  0.0528875299
## 87   0.019427201 -0.7472741460 -0.315263937 -0.339431116  0.8530010449
## 88   0.515099491  2.2369077013 -0.708746469 -0.099849514 -0.4085056983
## 89   0.396677405  1.0281156094  1.251735506  0.365048538  0.6113069945
## 90  -0.196958743  0.1727445012 -0.175979624  0.251242033  0.3075061692
## 91  -0.908803697 -0.4641643806 -1.195676014  1.524708105  0.6341433167
## 92  -0.459819133  0.2415520696 -0.701715520  0.943060828 -0.4390341268
## 93   0.577211676  0.8769549835  0.467237575 -0.293414270 -0.7410211870
## 94   0.376024108 -0.5759689750  0.918623238  1.180562016 -0.2256674920
## 95   0.376550480 -1.1251383134  0.986458836  0.529105777 -1.1761631521
## 96   0.256931250  1.0610395622 -0.053629478  0.064945845 -0.5656595143
## 97  -0.478982591 -0.4067158254 -0.469145662  1.271401627  1.3387050869
## 98  -0.564062512 -3.0245294479  0.224081729 -0.554508893  0.2526254534
## 99   1.600824809 -0.1890302916 -0.476698915 -0.651020429 -1.1351435908
## 100  0.031125975  0.5189074993  0.558725281  0.430966100 -0.2377379712
## 101  0.197998438  0.0167154008  0.111369110 -0.132114611 -0.7366617528
## 102 -0.232379694  0.3170869111 -1.303548212  0.056202797  0.0039380143
## 103  0.097994130 -0.0417656755 -0.142942833 -0.152476705  0.2511952063
## 104 -0.978807594 -0.0232077362  1.024213559 -0.137775845 -0.2087744303
## 105 -1.037444131 -0.2112538879  0.033504034  1.106887063 -0.2613662304
## 106  0.297656183  0.2983409313  0.139191347  0.529135533 -0.1804720323
## 107  0.267943255 -0.4792219363  0.621133158 -0.299252011 -0.0977380566
## 108 -0.528340518  0.1251328831 -0.768143809 -0.088742811  1.0350856613
## 109 -0.142842041 -1.8814894234  0.895453078  1.186341067 -0.0392106502
## 110  1.032007126 -0.3873793935 -0.816200335 -0.424840010  0.8279075380
## 111  0.481548479  0.3114823182  0.292619651  0.622543704  0.4464357392
## 112  1.559874683  0.5833313450  0.424954703  0.585170837  0.0450815216
## 113 -1.510634671  0.2747947549 -0.496823920  1.038737062  0.1047037030
## 114 -0.115316858  0.2975403823 -0.012049023  0.494542530  0.1300361673
## 115 -0.188075600  0.8888540550  1.141636781  0.988710888  0.6328114784
## 116  0.056360617  1.0870240618 -0.357582970 -0.380795621 -0.4688026328
## 117 -0.731441650 -0.2534189793  0.607429918 -0.043427608  0.4755427006
## 118  1.575533621 -0.3750519323 -0.273590252  0.282372467 -0.1540428813
## 119  0.002893875 -0.6734814665 -0.163531606 -0.087412681  0.0663117691
## 120  0.446413642 -0.1277354242 -0.996326871  1.533737482  0.9768585655
## 121  0.267340266 -0.5660987518 -0.007395508 -1.279686466 -0.7323835988
## 122  0.046445956  0.7468656629  0.483713407  0.247944485 -0.2913995915
## 123  0.909000719  0.0897831534  1.177838651 -0.947387266 -0.3197825387
## 124  0.629823071  0.2879453770  1.029217109 -0.552474310  1.3399238865
## 125 -0.794056705  0.3317744877  0.355197311  1.018422844 -0.9907731226
## 126  0.622477115 -0.5249701939 -0.121688716 -0.490384411  0.5245018888
## 127 -0.751432612  0.0410632906  0.737055324  0.247121500  0.2607815840
## 128 -0.909917129 -0.3612919060  1.024192187 -0.346690172 -0.0056423842
## 129  0.154926058 -1.4391681156  0.274585841  0.185280098 -0.0479047276
## 130  0.270625145  0.3443025149  0.360694788  0.564730189 -0.2459314922
## 131  0.748888428 -0.7342885254  0.021271498  0.153580439  0.2566140136
## 132  0.292263416  0.4171591028 -0.584429409  0.931877149 -1.0174449090
## 133  0.632725753  0.7066884287  0.401761592  0.397497447 -0.8849132904
## 134  0.082412656 -0.1684765550 -0.870702276 -0.460534180  0.4826390917
## 135 -0.499571994  0.8084684685  0.725699554 -0.085896325 -0.8420581965
## 136  1.781096755 -0.8817805695  0.475251084  0.458090033  0.1610472198
## 137  0.486212420  1.2972806649 -1.259504124  0.426123376  0.9838162454
## 138 -1.052839007 -0.1033355495 -0.698800981 -0.328668481 -0.3616124824
## 139 -0.827117215  0.0825104158  0.688979321  0.914761849  0.9162253019
## 140  0.311282220  0.4158344275  1.270788526 -0.325763084  0.1517838075
## 141 -0.612991740 -0.2019474897  0.355503758 -1.244776480 -0.2495189658
## 142 -0.114333649 -0.0227009135  0.406267180 -0.010405241  1.2048803881
## 143  1.878384008 -0.2393013201 -0.157397029 -0.808686716 -0.9757275257
## 144 -0.607143298  0.1189496401 -0.477891520 -0.166257131 -0.2144755379
## 145  0.739290331  0.2381621476 -0.765082706  0.684180982 -0.0171179900
## 146 -0.145260843 -0.1348441116  0.432561804  0.283733600 -0.3620050869
## 147 -0.086011284  0.5618417957  0.276456518 -0.770593330  0.3672118599
## 148  0.160227162 -2.1881068236  0.902234343  1.106876115 -0.0786894943
## 149  0.031317302  0.1911905163  0.005616693 -0.018958445  0.0881407007
## 150 -0.726166472 -0.0431326938 -0.531473520 -0.073684909 -0.0995940026
## 151  0.789761746 -0.0174189036  0.847593039  0.723763015  0.3713978512
## 152  2.037954543 -0.2982559638 -0.565114272 -0.486874526 -0.2751620212
## 153  0.128639109  1.2161735687  0.908866917 -0.771517783  2.0159239490
## 154 -1.533056562 -0.7886853127 -1.578448855 -1.027067669 -0.1558162169
## 155 -1.799206424  0.3517339788  1.006613812 -0.511938750 -0.6690267496
## 156 -1.745772166  0.6357702258 -0.328529303 -1.535686219 -0.0084052138
## 157 -1.727595126  0.2096404580 -0.379922081 -1.631281664 -0.3556658255
## 158 -2.376585351  0.8935729172 -0.498587445  0.560593037 -0.1535818719
## 159  1.005679461  0.1691497143  0.301254883  1.396244152  0.8544999510
## 160  0.358603585 -0.7299125978  0.855931458 -0.564462146  0.6768503139
## 161 -0.118277128  0.3147405380 -0.961954969 -0.370877751  1.7798329478
## 162  1.322369895  1.3216155305 -0.328367399 -2.185022759 -0.0006690793
## 163 -0.490946417 -0.2477650604 -0.394734903  0.947105811  0.0303566101
## 164 -0.323505427 -0.7698571887  0.749456412 -0.140540080 -1.0586996402
## 165 -0.024775395 -0.2833212994  0.373770439 -0.595502381  0.7588735967
## 166  1.096750958 -0.0400292467  0.109174495 -0.542275847 -0.5334434028
## 167 -1.665107558  0.3814373406 -0.019691055  1.080792101 -0.0472712677
## 168  0.121517841 -1.6336033878 -0.593843975  1.032200983 -1.1569982511
## 169 -0.549889731  0.1712785672 -0.611523409 -1.099377267 -0.7051790987
## 170  0.173090442 -0.3460925249  0.765095255 -0.297061213  0.8511220659
## 171 -0.322702786  0.6536319167  0.791574771 -0.362402839 -0.9256792672
## 172 -0.393904330  0.4091380943 -0.259342542  0.826594309  0.1533518369
## 173  0.637843045  0.5151152191  0.641350658 -1.049027385  0.0623796356
## 174  1.556299335  0.2068648506 -0.920435851  0.910946304  0.4296449544
## 175 -0.362008509  0.8741466793  0.951553236  0.081808646 -0.0697876936
## 176 -1.710189519  1.0325347910  0.412329823 -0.031140234 -0.3517095595
## 177 -0.909995025  1.4121049162 -1.210938149 -0.051017509 -0.0331009714
## 178  0.239525689 -0.6413809846  0.822266920 -0.555354028  0.2051302279
## 179  0.545524019  0.0655601494 -1.438160622  0.538839358  0.2856419443
## 180 -0.124850377 -0.3876590948 -0.089921253 -0.040303164 -0.0981735864
## 181  0.403768501 -0.5956669180 -0.734455947 -0.275493242  0.3301105084
## 182 -0.132930313 -0.3766394866 -0.187203238 -0.064829097 -0.0839396096
## 183  0.016270698  0.7615497571  0.333919451  0.171045051 -0.2624416848
## 184 -0.224043337  0.2646391701  0.570084353  0.095086855 -0.3850995679
## 185  0.147757152 -0.4780702868 -0.895359681 -0.652032973  0.6727709000
## 186  0.193616175 -0.4240181500 -0.498121267 -0.720241421 -0.3232495839
## 187 -0.034761097  1.1457298699  0.586766276 -0.625570708  0.6892305938
## 188  0.504482451  0.5496962695  0.060856072 -0.847121852 -0.7707882356
## 189 -0.650616269 -0.1605567900  0.414551028 -2.110531901 -0.1496008604
## 190 -0.182798626  1.6411241358  1.044213913  0.110493834  0.2288751125
## 191  0.095969948  0.8016115611  0.042308039  0.010436164 -0.1049633741
## 192 -0.366156628  0.7496332500  0.768361136 -1.091461924  0.7148505058
## 193 -0.946409204 -0.3152183738  0.150414025 -1.053778779  0.7113997225
## 194 -0.855672835 -0.9830093268 -0.905832846 -0.409623569  0.1492982261
## 195  0.325176088 -0.6070675912  0.367549686  0.061677189  0.0541561124
## 196  0.794881574 -0.8748651352 -0.084748319  0.270197773  0.0146265993
## 197 -0.066920247 -0.1862714119  0.098864439  0.147105215  0.4261859754
## 198  0.570324710  2.0238937521 -1.044359363 -0.273356272 -0.2185264856
## 199  0.425186441  0.6429611071  0.491994328 -0.126800674  1.0069575413
## 200 -0.309246961  0.7596944788  0.686920137  0.799763529 -0.2162877586
## 201 -0.926207624 -0.3478009217 -1.355300510  1.578113090  0.5935029616
## 202 -0.435040531  0.4237204416 -0.745279545  1.175313970 -0.5592385296
## 203  0.452443320  1.0957245385  0.142243809 -0.388730863 -0.7838865288
## 204  0.419772768 -0.9714967884  0.485821261  0.774175656  0.1081471239
## 205  0.175739436 -0.6851285663  0.715121492  0.516934869 -1.3528110796
## 206  0.353103360  0.5024938497 -0.823726838 -0.469077034 -0.0738754850
## 207 -0.616674826  0.1076888698  0.048842036  1.623576983  0.9385118280
## 208 -0.932014894 -2.3782729327 -0.056710547 -0.746252808 -1.0047732584
## 209  1.560076315 -0.0806846266 -0.101208215 -0.548504487 -1.2679059152
## 210  0.177987430 -0.3405525381  0.069584376 -0.255456285  0.3831698686
## 211  0.290925203 -0.4797676870  0.097365997 -0.458753115 -0.4330577300
## 212 -0.197654486  0.2195844532 -1.364133168  0.014767142  0.0697480723
## 213  0.033115596  0.4977976943  0.277185030  0.357443913 -0.1692388424
## 214 -0.986944360 -0.0632916842  1.195268464 -0.162507838 -0.2130873890
## 215 -0.885201565 -0.8401300969 -0.235047500  0.715123819  0.1615237371
## 216  0.348346118 -0.0255630837 -0.265224647  0.217261282  0.0980469217
## 217  0.219225392 -0.3749311471  0.813013327 -0.253789639 -0.1893930475
## 218 -0.580699335  0.4949571942 -0.222702935  0.295336073  0.6989844827
## 219 -0.324346284 -1.3337935698  0.998841732  1.400331616 -0.3667381814
## 220  0.292793239 -0.5584445302  0.117974067 -0.004227517  0.0807831232
## 221  1.022770651  0.1527312235 -0.371180305  1.281589722  0.9916750779
## 222  0.465861696 -1.1847956071  0.607637361 -0.864458757  0.9942057110
## 223 -0.424516730  1.4748814174  0.145181171  0.420214420  0.8878891898
## 224  1.236438417  1.7300181032  0.383479681 -1.797487236 -0.3845053731
## 225 -0.426387323 -0.2842011807 -0.688413707  0.984933178  0.0919241125
## 226 -0.263850500 -0.9207747960  0.901682146 -0.143776831 -1.0068171990
## 227 -0.162814971  0.5436072760  1.690537431  0.239060114 -0.0051335613
## 228  1.026434521  0.1900517074  0.077777001 -0.454886610 -0.6582377293
## 229 -1.572773111 -0.0312910426 -0.288500239  0.789657126  0.2507442514
## 230  0.036653223 -1.0775967170  0.277635073  1.607073041 -1.6704573397
## 231 -0.760711421  0.5801334609 -0.853926932 -1.158985637 -0.8636755088
## 232  0.224797306 -0.8638491677  0.369310689 -0.806783880  1.2564088524
## 233 -0.256109481  0.0813377143  0.160075683 -0.944625884 -0.4426724802
## 234 -0.500478173  1.1402854283  0.940682998  1.603648258 -0.5339839208
## 235  0.420557609  1.1757651232  1.405814095 -0.660944846 -0.4584058641
## 236  1.601474335  0.0329770609 -0.786863332  0.850110349  0.5049464856
## 237 -0.245442814  0.5299043586  0.123567074 -0.198453838  0.2846141257
## 238 -1.677910380  0.9370002172  0.587961195 -0.028877664 -0.3326711026
## 239 -0.615963168  0.4614410046 -1.373119458 -0.462593734  0.5385699125
## 240  0.346190183 -0.1741353115 -1.640682285  0.219620922 -0.4347494070
## 241 -0.237700953 -1.8269571358 -1.733722502 -0.868267167  0.0739759153
## 242  0.189743967 -0.4365589058 -0.484810381 -0.440615878  0.5517758465
## 243 -0.157734030  1.3944431466 -1.315420940 -1.163315747 -1.0278137201
## 244  1.482778302 -1.2292871843  0.735433828 -0.310230712  0.2165680484
## 245  0.458353115  1.2794759823 -1.481894590  0.305867734  1.0478414078
## 246 -0.561798075  1.1599444136 -0.106549811  0.174440364 -0.5614477491
## 247 -0.904030686  0.1899898851  0.077693633  0.746239059  0.9884091324
## 248  0.367306846  0.0797105468  0.421658844 -0.727251810  0.5237866907
## 249 -0.771447964  0.3220145131  0.421694621 -1.015059403 -0.5611796464
## 250  0.891226655  1.8559091541  1.012247198  0.055194895 -0.9096856467
## 251  1.865768690 -0.2969116509 -0.060634134 -0.875628676 -0.9524645024
## 252 -0.460426027 -0.7028922394 -1.480131889 -0.915330523  0.4818986921
## 253  0.383069666  0.0729546428  0.084302734  0.102023258 -0.1799652501
## 254 -0.073701024 -0.5385788237 -0.284734897 -0.129813506  0.0242731252
## 255 -0.316718368  1.3263872034  0.646147689 -0.380331569 -0.1411549227
## 256 -0.020055754 -1.7066672359  1.308291456  1.314337165 -0.4218148172
## 257  0.099230582  0.0633414172 -0.089809685 -0.030062396  0.1705910065
## 258 -0.814719325  0.3554712920 -0.482169057  0.167179178 -0.3464488494
## 259  0.827465657 -0.2784515308  0.408041681  0.443426503  0.6190726633
## 260  1.969911006  0.1981480175 -0.131559676 -0.025757074 -0.6685676214
## 261  0.120692741  1.5520772439  1.851214993 -0.252163607  1.6108503758
## 262  0.382435126 -0.0915046435  0.031776181 -0.399960814  0.6689254912
## 263 -1.094660807  0.5313274642 -0.723942851  0.793217363 -0.4923627949
## 264  0.077558875  1.0730493255 -0.864140025 -0.451585611 -0.3669914933
## 265 -0.792476333 -0.1982225738  0.358157169 -0.161823863  0.5066678723
## 266  1.553818534 -0.4152766906 -0.754771835  0.100342799 -0.0263940820
## 267  0.786240415  0.5920760463 -0.296554785  0.146965215  0.8331283743
## 268 -0.077097448 -0.1064969348  0.735943782 -0.312441464 -0.3501374412
## 269 -0.507108198 -0.1399924983  1.449425933 -0.110453136 -0.6621996038
## 270  0.040436218  0.8904793243  1.394424602  0.565017503 -0.5631495248
## 271  0.271097474 -0.1892803429 -0.938504400  0.190741482  0.2747592430
## 272  0.074050682  0.1269508821 -0.024944975 -0.003253330  0.1234850640
## 273 -0.931853006  1.0078033725  0.209204840  0.739747383 -0.8785993809
## 274  0.836197278  0.0005452163 -0.200324353 -0.003385652 -0.5181722760
## 275 -0.841050307 -1.1692393307 -0.517406569 -0.715403414  0.1361235206
## 276 -0.983023515 -0.1041939949  1.271501292 -0.181852971 -0.2020560780
## 277 -0.801581787 -0.5012883274  1.399310331 -0.619467237  0.3217333923
## 278  0.235167642  0.0761654172 -0.868124389 -0.030755816  0.1837052038
## 279  0.259645931 -0.7659212831 -0.171331327 -0.771443767  0.2503776820
## 280  0.386626612  0.0020122656 -1.394599751  0.535355543 -0.6125133511
## 281  0.802480244 -0.1790725087 -0.588888791 -0.368026445 -0.1555218514
## 282  0.482401592  0.8485498995 -0.439878351  0.187371367 -0.9810781952
## 283  0.133037414  0.6534827324 -1.212225499  0.499259150 -0.6413672907
## 284  0.406502194  0.7165172399  0.480778116  0.925558289  0.1639291407
## 285 -0.857974639 -0.6741941727  0.840754566 -0.600815722  0.2219338890
## 286  0.038978935 -0.7220043659  0.586611893  0.752720450 -0.5492553667
## 287  0.400500823 -0.3586637134 -0.511835579 -0.069931664  0.3513372646
## 288  0.822793804 -1.1842067114 -0.215174410 -0.208041555  0.5787408975
## 289  0.367378840  0.0070424388 -1.070586440  0.564778180 -0.6732674459
## 290  0.707731574  0.3200376804 -0.202871587  0.031149299 -0.5331046573
## 291 -0.081437579  0.6813613159  0.423020726  0.339802365 -0.2840377311
## 292 -0.448238235  0.5883060329  0.080163844 -0.336205536 -0.5854681151
## 293  1.782082642 -0.8786251058  0.424369024  0.453352217  0.1686013563
## 294  0.262999653  2.5161366718  0.184353081  1.516995025 -0.0388854969
## 295 -1.028991209 -0.2410878726 -0.813808730 -0.445286831 -0.2550268203
## 296 -0.767768447 -0.1184498761 -0.336592138  0.625874697  1.2319341578
## 297  0.424298678 -0.1658003787  0.354749610 -0.877756151  0.6822191559
## 298 -0.583145614 -0.3361529386  0.012495691 -1.390367906 -0.1025393108
## 299 -0.021967799 -0.5455360842 -0.094936125 -0.461983720  1.6215068235
## 300  1.938133198 -0.6013023488 -0.357609883 -1.101025575 -0.7146842916
## 301 -0.568533563 -0.1138279703 -0.613242911 -0.355154778 -0.0453825308
## 302  0.737361526  0.1736037657 -0.361233504  0.692900730 -0.0526630204
## 303 -0.126718864 -0.2544281997  0.408186660  0.192943852 -0.2835720653
## 304 -0.061479981  0.4313114021  0.099934079 -0.890448988  0.4808252877
## 305  0.093734175 -1.8826517649  1.632717238  1.431294242 -0.4038404559
## 306  0.087368328 -0.0350587299 -0.772962725 -0.292136488  0.3733408245
## 307 -0.674268055 -0.2830235204 -1.093907597 -0.326910311  0.1536629841
## 308  0.814679485 -0.1524666351  0.681117266  0.601996141  0.4859256479
## 309  1.875453301  0.5883067607  0.490080068  0.307284192 -1.0199760971
##             PC16         PC17
## 1   -0.204699168  0.399778790
## 2    0.045288943  0.292915024
## 3   -0.271595154 -0.814045516
## 4   -0.371673537  1.078203419
## 5    0.734034423  0.516096799
## 6    0.370839736  0.464690533
## 7   -0.322143489  0.050306784
## 8    0.531051672  0.194644777
## 9   -1.124665269 -0.473960208
## 10   0.076492553  0.033336741
## 11  -0.534141622 -0.128982341
## 12   0.084037407 -0.456830857
## 13   0.189629446  0.456895464
## 14  -0.016716439 -0.021511422
## 15   0.006422442 -0.329564249
## 16  -0.225723824 -0.788232416
## 17   0.487690414 -0.355745563
## 18  -0.216253994  0.281111017
## 19  -0.357368372 -0.574817902
## 20  -0.121585264  0.153361961
## 21  -0.325279346  0.341539699
## 22  -0.249217026 -0.517074387
## 23  -0.474336582  0.001382573
## 24   0.020601136 -0.029383874
## 25  -0.421748563 -0.176386698
## 26  -0.375057468  0.459319241
## 27   0.157050749  1.283191589
## 28   0.172160415 -1.177121386
## 29   0.840632915  0.308201578
## 30   0.546906491  0.990041317
## 31   1.833637726  0.602301402
## 32   0.899009190 -0.685671003
## 33   0.778795299  0.192681525
## 34   0.282663097  0.192190653
## 35  -0.281726780 -0.102251797
## 36   0.404702630  0.315448071
## 37   0.252701007 -0.080408534
## 38   0.835870432 -0.173405499
## 39   0.794453324 -0.901139864
## 40  -0.664108490 -0.302257112
## 41  -0.699334673 -0.772619337
## 42   0.302214498  0.526431365
## 43   0.215644055  0.008363015
## 44   1.218170500 -0.374050417
## 45  -0.107189826  1.558186080
## 46  -0.014697978 -0.110994738
## 47  -0.314501834  1.085094010
## 48  -0.453323188  1.568209576
## 49   0.371135730 -0.880906339
## 50   0.038378647 -1.504845090
## 51  -0.190277899 -0.215343711
## 52   0.571180847 -0.485102183
## 53  -0.795216391  0.307609636
## 54   0.101171607 -0.457206584
## 55  -0.836682394  1.227393045
## 56  -0.761838666  0.044936466
## 57  -0.093377912  0.519556971
## 58  -0.085545972  0.334201010
## 59   0.820792154  0.214839663
## 60   0.108966172 -0.162975362
## 61  -0.542958636  1.037635542
## 62  -1.090814185 -0.173869707
## 63   0.397950756  0.601928262
## 64  -0.286457614 -0.316048608
## 65   1.423427877  0.100505316
## 66  -1.311470262 -0.340525215
## 67  -0.360979053  0.384060109
## 68   0.046545960  0.364930671
## 69   0.851869088  0.039331283
## 70   0.125575693  0.027204718
## 71   0.339668208  0.511883358
## 72   0.135095885 -0.227962988
## 73  -0.161028009 -0.359990351
## 74  -0.151488592  0.364242693
## 75   0.032547772 -0.019961277
## 76  -0.125258951 -0.040086038
## 77  -0.314385878 -0.543428311
## 78  -0.335717440  0.228175597
## 79   0.400994735 -0.072763914
## 80  -0.528254127  0.151448992
## 81   0.139513375  0.283297565
## 82  -0.005952746  0.259756203
## 83   0.220449326  0.205910512
## 84   0.821389639 -0.280463409
## 85  -0.616768168 -0.143967535
## 86   0.587250538  0.095098054
## 87  -0.057818756 -0.333248457
## 88  -0.618241629  0.030801222
## 89   0.262114853  0.284029297
## 90  -0.441595058  0.570186068
## 91   0.546853402  0.247395413
## 92  -0.954452414 -0.237225566
## 93  -0.690367526  0.648356547
## 94   1.196418062 -0.755162981
## 95  -1.025634831  0.626103061
## 96  -0.491732734 -0.231372581
## 97   0.162249355  0.180426095
## 98   0.601243917 -0.104024116
## 99  -1.217306954 -0.042251874
## 100  0.210795257 -0.266528766
## 101  0.009178791 -0.140306083
## 102 -0.239832184 -0.505299089
## 103 -0.001081145  0.061331010
## 104  0.225753874  0.024185581
## 105 -0.423907862  0.044826848
## 106 -0.049813183  0.066391359
## 107  0.144666199  0.249381777
## 108  0.288291683  0.147150980
## 109  0.683932546 -0.766405649
## 110 -0.165238363  0.413606088
## 111 -0.311500803  0.275308649
## 112  0.470357058  0.841243335
## 113  0.222169322 -1.078565979
## 114 -0.168079224  0.872922772
## 115  0.877633521  1.155793976
## 116  0.248481964  0.515447773
## 117 -0.215599949  0.058770936
## 118  0.514993586  0.210590031
## 119 -0.226150793 -0.086942561
## 120  0.289380434  0.313280968
## 121  0.215127207 -0.235851294
## 122  0.018379895 -0.540713487
## 123 -0.445011923 -1.187395940
## 124 -0.197477228  0.266806473
## 125 -0.289242777 -0.037798448
## 126 -0.565139828 -0.738008042
## 127 -0.159623044 -0.074763111
## 128  0.075685920  0.058279950
## 129 -0.639909303  0.323712286
## 130  0.029766279  0.032157735
## 131  0.251431807  0.393080370
## 132  0.099890861 -0.888438144
## 133  0.278208194  0.028194637
## 134 -0.035768643  0.342225755
## 135 -0.465900314 -0.053961025
## 136 -0.579918745 -0.349760333
## 137  0.000772863  0.151658109
## 138  0.209223668 -1.243826974
## 139  0.869070173  0.233877079
## 140  0.805399365  0.872283165
## 141  0.341425105  0.022592252
## 142 -0.684397168 -0.936264140
## 143  0.869141848 -0.006288726
## 144 -0.404210072 -0.522821842
## 145  0.676296036 -0.021386986
## 146  0.152334617 -0.236617040
## 147  0.100548266  0.546407053
## 148 -0.614292886  0.646342147
## 149  0.157997524  0.030636773
## 150 -0.396764299 -0.190573406
## 151 -0.644069677 -0.846298375
## 152  0.284353292  0.503158969
## 153  0.173424869  0.019842343
## 154  0.044405912 -0.388242074
## 155  0.824834606  0.325438074
## 156  0.121962865 -0.861216712
## 157 -0.442513188  0.702610115
## 158  0.793495320  0.334082201
## 159  0.447669504 -1.216843843
## 160  0.090886418 -1.371108370
## 161 -0.438017503  0.002962693
## 162  0.541409695 -0.450589729
## 163 -0.820401346  0.677621810
## 164  0.226252313 -0.216161914
## 165 -0.677481397  1.415588471
## 166 -0.583691233  0.119191040
## 167  0.293109180  0.174793193
## 168 -0.203669862  0.239594626
## 169  0.743351273  0.219123542
## 170  0.130802257 -0.400058587
## 171 -0.410579567  0.611738612
## 172 -1.026212619 -0.272878294
## 173  0.242101208  0.488238862
## 174 -0.288948646 -0.279987488
## 175  1.601354083 -0.114113845
## 176 -1.520591312 -0.365248874
## 177 -0.085103098  0.421068268
## 178  0.047903515  0.346408715
## 179  0.290577969  0.257721538
## 180  0.058594121 -0.016260362
## 181  0.351179366  0.395519794
## 182  0.067019098  0.018984832
## 183  0.069867765 -0.454941763
## 184  0.068081891  0.334040887
## 185 -0.180412417  0.376233283
## 186 -0.039127144  0.230944364
## 187 -0.461598407 -0.299418857
## 188 -0.863571623  0.415674312
## 189  0.164826381 -0.745791996
## 190  0.055938829 -0.226902271
## 191 -1.130935409  0.447494847
## 192 -0.780931794 -0.127862513
## 193 -0.218573295 -0.492468351
## 194 -0.164408869 -0.368908455
## 195 -0.723395579  0.067538846
## 196  0.685196206  0.204171257
## 197  0.169355098 -0.549958598
## 198 -0.769993878  0.122808536
## 199  0.128325234  0.614367708
## 200 -0.115885447  0.264880595
## 201  0.569809145  0.268030342
## 202 -1.012129894 -0.350160623
## 203 -0.449618464  0.852052206
## 204  1.060227957 -0.534824136
## 205 -0.614394865  0.846168128
## 206 -0.773683331  0.063697140
## 207  0.510641502  0.044842721
## 208  0.539028601 -0.851370448
## 209 -1.093386790 -0.122726928
## 210 -0.155246654  0.001096426
## 211 -0.194613598 -0.072297240
## 212 -0.321072705 -0.504598778
## 213  0.179998006 -0.184224234
## 214  0.259444768  0.009943970
## 215 -0.780618138  0.139516314
## 216 -0.198320989  0.234820841
## 217  0.268641865  0.234126153
## 218  0.453731649 -0.077289733
## 219  1.088579218 -0.729502626
## 220 -0.676442863  0.168806418
## 221  0.347355852 -1.056801166
## 222 -0.165990170 -1.283069689
## 223  0.332638512 -0.293672149
## 224  0.795452124 -0.679781217
## 225 -0.988260241  0.662611902
## 226  0.110787399 -0.291810588
## 227 -0.252893278  0.923464117
## 228 -0.433616613  0.144755671
## 229  0.066773967  0.275017663
## 230  0.063241523 -0.101200129
## 231  1.179012497  0.462607684
## 232 -0.019352945 -0.148293626
## 233 -0.615282088  0.926318797
## 234 -0.681058673 -0.744278153
## 235  0.786713435  0.356755296
## 236 -0.374744887 -0.315348333
## 237  1.269945960  0.064941224
## 238 -1.574325649 -0.425168932
## 239 -0.740202720  0.388446323
## 240 -0.117226699 -0.428558305
## 241  0.955826543 -0.268608022
## 242 -0.232986784  0.174246513
## 243 -0.030911579 -0.178010067
## 244 -1.116037385 -0.443587411
## 245  0.040368748  0.267750892
## 246  1.404264474 -1.478292614
## 247  0.978839680  0.483021714
## 248  0.603511293  1.157426119
## 249  0.692486224  0.040663628
## 250 -0.722358199 -0.980492359
## 251  0.905558470  0.015177064
## 252 -0.818092266 -0.133033980
## 253  0.321527445 -0.257408901
## 254 -0.070998352  0.016638914
## 255  0.637360258  0.497985009
## 256 -0.183950774  0.629102932
## 257  0.001359994 -0.002573657
## 258 -0.199281757 -0.231513525
## 259 -0.767591488 -0.674397629
## 260  0.473512663  0.278870895
## 261  0.279643315 -0.373044027
## 262  1.231233143 -0.616917441
## 263  1.196629303  0.206480172
## 264  0.154833871  0.622433628
## 265 -0.106378218  0.206223917
## 266  0.516903811  0.396282048
## 267 -1.619758037 -0.272082445
## 268  0.326323508 -0.089511243
## 269 -0.174273385 -0.580481396
## 270  0.117172450 -0.841650045
## 271  0.058390380  0.788983893
## 272  0.062226434 -0.005549539
## 273  0.120922819 -0.511551264
## 274 -0.104788706 -0.658045736
## 275  0.155305470 -0.417142635
## 276  0.258037515  0.001018338
## 277 -0.471111047 -0.560894424
## 278 -0.009003091  0.546602298
## 279  0.087872999  0.607421705
## 280 -0.181710770 -0.644080424
## 281 -0.184704565  0.404085944
## 282  0.381975583 -0.300021491
## 283 -0.599984450 -0.026298504
## 284 -0.130302106  0.170677295
## 285 -0.054769022  0.159784347
## 286 -0.357835410  0.115076387
## 287 -0.335197519  0.362168104
## 288  0.068117172  0.532982330
## 289 -0.109459288 -0.700975579
## 290  0.057996353  0.237331002
## 291  0.442745185 -0.109642684
## 292 -0.638324403  0.131842402
## 293 -0.586836031 -0.339105240
## 294  0.622801658 -0.405256743
## 295  0.146444590 -1.191554915
## 296  0.643560584  0.500112321
## 297  0.473122824  1.188323428
## 298  0.244203227  0.124670211
## 299 -0.932773979 -0.723538859
## 300  0.720091571  0.108483530
## 301 -0.501085666 -0.447556210
## 302  0.718340959 -0.098268391
## 303  0.109617474 -0.207952469
## 304  0.030515055  0.610897882
## 305 -0.400852865  0.425130764
## 306 -0.037178820  0.247090067
## 307 -0.562633443 -0.019336438
## 308 -0.714004235 -0.783153726
## 309  0.737576367  0.096973111
# Means of scores for all the PC's classified by Survival status
tabmeansPC <- aggregate(cancerp_pca[,2:15],by=list(LUNG_CANCER=cancer$LUNG_CANCER),mean)
tabmeansPC
##   LUNG_CANCER         PC1        PC2        PC3       PC4          PC5
## 1           0  0.33366607 -1.0169661 -0.7839497 -1.097169  0.010636897
## 2           1 -0.04819621  0.1468951  0.1132372  0.158480 -0.001536441
##          PC6         PC7         PC8         PC9        PC10        PC11
## 1  0.8480279 -0.13586975  0.09232115 -0.14776307 -0.07819061 -0.18188979
## 2 -0.1224929  0.01962563 -0.01333528  0.02134355  0.01129420  0.02627297
##          PC12        PC13        PC14
## 1  0.11610476 -0.21705424  0.11768416
## 2 -0.01677069  0.03135228 -0.01699882
# The output shows that for most of the principal components (PC2 to PC14), the mean scores are higher for the non-survivors compared to the survivors. However, for PC1, the mean score is higher for the survivors compared to the non-survivors.This suggests that the first principal component may be particularly important in differentiating between survivors and non-survivors of lung cancer. The other principal components may also provide some information on differences between the two groups, but their importance may be more limited.

tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$LUNG_CANCER)),]
tabmeansPC
##   LUNG_CANCER         PC1        PC2        PC3       PC4          PC5
## 2           1 -0.04819621  0.1468951  0.1132372  0.158480 -0.001536441
## 1           0  0.33366607 -1.0169661 -0.7839497 -1.097169  0.010636897
##          PC6         PC7         PC8         PC9        PC10        PC11
## 2 -0.1224929  0.01962563 -0.01333528  0.02134355  0.01129420  0.02627297
## 1  0.8480279 -0.13586975  0.09232115 -0.14776307 -0.07819061 -0.18188979
##          PC12        PC13        PC14
## 2 -0.01677069  0.03135228 -0.01699882
## 1  0.11610476 -0.21705424  0.11768416
#This output is useful for comparing the mean scores of the different principal components based on the survival status of the patients. The negative values for some of the principal components suggest that these components have an inverse relationship with the survival status of the patients.

tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
##                 2           1
## PC1  -0.048196210  0.33366607
## PC2   0.146895102 -1.01696609
## PC3   0.113237181 -0.78394971
## PC4   0.158479973 -1.09716904
## PC5  -0.001536441  0.01063690
## PC6  -0.122492912  0.84802785
## PC7   0.019625631 -0.13586975
## PC8  -0.013335277  0.09232115
## PC9   0.021343555 -0.14776307
## PC10  0.011294199 -0.07819061
## PC11  0.026272969 -0.18188979
## PC12 -0.016770687  0.11610476
## PC13  0.031352279 -0.21705424
## PC14 -0.016998823  0.11768416
#The rows represent each of the PCs and the columns represent the two groups. For example, the first row represents the mean values of PC1 for both groups. The value in the first row and second column (-0.048196210) indicates that the mean value of PC1 for the group classified as 2 is negative and smaller than the mean value of PC1 for the group classified as 1, which is represented by the value in the first row and first column (0.33366607).
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$LUNG_CANCER))
tabfmeans
##                 1           0
## PC1  -0.048196210  0.33366607
## PC2   0.146895102 -1.01696609
## PC3   0.113237181 -0.78394971
## PC4   0.158479973 -1.09716904
## PC5  -0.001536441  0.01063690
## PC6  -0.122492912  0.84802785
## PC7   0.019625631 -0.13586975
## PC8  -0.013335277  0.09232115
## PC9   0.021343555 -0.14776307
## PC10  0.011294199 -0.07819061
## PC11  0.026272969 -0.18188979
## PC12 -0.016770687  0.11610476
## PC13  0.031352279 -0.21705424
## PC14 -0.016998823  0.11768416
# Standard deviations of scores for all the PC's classified by Survival status
tabsdsPC <- aggregate(cancerp_pca[,2:15],by=list(LUNG_CANCER=cancer$LUNG_CANCER),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$LUNG_CANCER))
tabfsds
##              0         1
## PC1  1.1609600 1.7524300
## PC2  1.5776135 1.3108022
## PC3  1.3045548 1.2613646
## PC4  1.1200050 1.1441594
## PC5  1.1304709 1.1454427
## PC6  1.0748310 0.9720025
## PC7  0.8220952 0.9970793
## PC8  1.1019348 0.9205512
## PC9  0.9200968 0.9004061
## PC10 0.6403545 0.8712853
## PC11 0.8557198 0.7849393
## PC12 0.7749977 0.7640128
## PC13 0.6910340 0.7296813
## PC14 0.6131616 0.7318746
t.test(PC1~cancer$LUNG_CANCER,data=cancerp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC1 by cancer$LUNG_CANCER
## t = 1.7817, df = 66.117, p-value = 0.07939
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -0.04603076  0.80975531
## sample estimates:
## mean in group 0 mean in group 1 
##      0.33366607     -0.04819621
t.test(PC2~cancer$LUNG_CANCER,data=cancerp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC2 by cancer$LUNG_CANCER
## t = -4.3933, df = 45.892, p-value = 6.533e-05
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.6971443 -0.6305781
## sample estimates:
## mean in group 0 mean in group 1 
##      -1.0169661       0.1468951
t.test(PC3~cancer$LUNG_CANCER,data=cancerp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC3 by cancer$LUNG_CANCER
## t = -4.0313, df = 48.83, p-value = 0.0001939
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.3444652 -0.4499086
## sample estimates:
## mean in group 0 mean in group 1 
##      -0.7839497       0.1132372
t.test(PC4~cancer$LUNG_CANCER,data=cancerp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC4 by cancer$LUNG_CANCER
## t = -6.5267, df = 50.159, p-value = 3.26e-08
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.6420402 -0.8692579
## sample estimates:
## mean in group 0 mean in group 1 
##       -1.097169        0.158480
t.test(PC5~cancer$LUNG_CANCER,data=cancerp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC5 by cancer$LUNG_CANCER
## t = 0.062756, df = 49.951, p-value = 0.9502
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -0.3774538  0.4018004
## sample estimates:
## mean in group 0 mean in group 1 
##     0.010636897    -0.001536441
# The output shows that the p-value is 0.07939, which is above the significance level of 0.05, indicating that we cannot reject the null hypothesis of no difference in means between the two groups at the 5% significance level for PC1. Similarly we can do this for other PC's as well. 

plot(eigen_cancer, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")

plot(log(eigen_cancer), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")

print(summary(cancer_pca))
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     1.6925 1.3991 1.29946 1.21349 1.14175 1.03533 0.97690
## Proportion of Variance 0.1685 0.1152 0.09933 0.08662 0.07668 0.06305 0.05614
## Cumulative Proportion  0.1685 0.2837 0.38299 0.46961 0.54629 0.60934 0.66548
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.94401 0.90315 0.84528 0.79577 0.76541 0.72853 0.71848
## Proportion of Variance 0.05242 0.04798 0.04203 0.03725 0.03446 0.03122 0.03037
## Cumulative Proportion  0.71790 0.76588 0.80791 0.84516 0.87962 0.91084 0.94121
##                           PC15    PC16    PC17
## Standard deviation     0.63523 0.56479 0.52625
## Proportion of Variance 0.02374 0.01876 0.01629
## Cumulative Proportion  0.96495 0.98371 1.00000
#The first three PCs (PC1, PC2, and PC3) account for a total of 38.5% of the variance in the data. The first seven PCs (PC1-PC7) together explain 66.5% of the variance, and the first 14 PCs explain 94.1% of the variance. Therefore, it appears that most of the variance in the data is captured by the first few PCs. The summary also indicates that the standard deviation of each PC decreases as the PC index increases. This means that the amount of variation explained by each PC decreases as the index increases. The proportion of variance and cumulative proportion of each PC follow a similar pattern.
cancer_pca$x
##                 PC1          PC2         PC3          PC4          PC5
##   [1,] -0.646329947  0.332751806 -0.44274023  2.859184418  0.122598754
##   [2,] -0.610508061  0.058855781  0.83878638 -1.618262677 -1.600337930
##   [3,] -0.749550736 -1.504421159  2.66955055 -0.633003311 -0.554423032
##   [4,]  1.096019632  2.420201554 -1.33296429 -0.623882219 -1.620199492
##   [5,]  0.036188930 -1.476567174  1.06322075 -0.297399332  0.877535001
##   [6,] -0.532567242 -1.816704968  1.59490775  0.295408659  1.957759532
##   [7,] -2.543550172 -0.443750841  0.65879801 -0.490274648 -2.164652907
##   [8,]  2.572207921 -0.611692066  0.98184227 -0.400242160 -2.014776748
##   [9,]  1.272938608 -1.748902681 -2.03358144 -0.603715268 -0.190135930
##  [10,]  1.396823254  2.844502270 -1.74624933 -0.548914628 -0.481234509
##  [11,]  2.064989024 -1.179537297  0.77287410  1.619240317  0.200840281
##  [12,] -3.094017924 -0.236356800  0.18223710  0.351212010  1.270144781
##  [13,]  0.217887666 -2.889346007 -0.91100600 -1.432307481 -1.045267875
##  [14,] -3.138457875 -0.373951998 -0.53082600  0.580383563 -1.106225675
##  [15,] -2.644849262  1.404467949 -1.44318316  0.143100628  0.232452899
##  [16,]  1.650628200 -0.224745382  3.27395413 -0.093011818 -0.017887882
##  [17,] -2.832351242  0.682525475 -0.73821564 -0.010801951  0.679269335
##  [18,]  1.926614145  2.783633537 -0.57374848 -1.250303351 -1.057854292
##  [19,]  2.058726013 -1.588839942  1.68092889 -0.276981888 -0.505797399
##  [20,]  0.277622753 -2.858606054 -0.42259847 -2.045803131  0.939549144
##  [21,]  3.229605844 -1.107957864  0.54769701 -1.054795775 -1.494603821
##  [22,]  1.856494117  1.281078425  1.72529424  0.500791276  1.185679005
##  [23,] -0.050480044 -3.127406007 -3.04980327 -1.990025288 -0.705699392
##  [24,] -3.114648178 -0.180587030  0.10426359  0.266726364 -1.323963055
##  [25,]  0.277610744  3.357861077  0.49327829  0.917467589  0.437189391
##  [26,] -0.593103049  0.624184222  0.58814373  2.058674696 -0.508287510
##  [27,]  0.798726715  0.817444755  0.93374653 -0.444838292 -2.523918618
##  [28,] -1.483179713 -1.292781315  1.00754634  0.715640195  0.065334512
##  [29,]  1.135171580  0.783408309 -1.75430086  0.465724163 -0.417313447
##  [30,] -1.513992882 -1.471854090 -0.71445396  1.239531591  0.767188290
##  [31,]  1.249804903 -1.966549418 -1.89456009 -0.936322757 -0.643651435
##  [32,] -1.015659657  1.565562602 -1.96636100  0.688684179 -1.044736566
##  [33,]  1.959456710 -0.179323614 -1.66903462 -0.161407143 -1.632984057
##  [34,]  2.332965976  0.401390187  0.14559217 -1.127745419 -1.393041621
##  [35,]  1.785139801  1.845010472  0.27438022 -1.498888257 -1.437361903
##  [36,]  2.803119610 -0.463091900 -0.61631147 -1.129814399 -0.672500165
##  [37,] -0.906183428 -0.252869061  0.60868898 -0.552044454  0.490794665
##  [38,]  0.625607571 -1.096717211 -0.29615831 -1.482097111  1.247479925
##  [39,] -0.980782008 -0.452929695 -1.00809976 -1.791086031 -0.953341909
##  [40,] -2.531034433  1.054359249 -2.75170356  0.062941767  1.314619757
##  [41,] -1.849943675 -0.036969503 -0.70926167  0.528593229 -1.528261831
##  [42,] -0.768929068  0.787507023 -0.50866975  0.164717527  1.435220054
##  [43,]  1.593703995  0.429036798  1.52983078 -0.546232596  1.925341348
##  [44,] -1.913272210  0.172794143  0.20744605 -0.721150606 -1.789307797
##  [45,]  1.543800949  0.459571313 -1.73845136  0.640217881  2.124908844
##  [46,]  0.292377930  1.094376928  0.98377124  1.985566661 -0.599839321
##  [47,] -0.251600030  0.717276148  0.11116195 -0.575662628 -0.910947467
##  [48,]  0.254838293  0.616454646  0.11114292  1.765377472 -0.055649992
##  [49,]  0.179367433  1.125141361  2.32349723 -0.520119821  0.277971205
##  [50,]  0.952911843  1.162517658 -0.71030972 -2.443376329  1.135427261
##  [51,] -0.851848170  0.904980380  1.94819723 -2.525220801  0.637015235
##  [52,]  0.301087025 -0.841444915 -0.33470279  0.020924532 -0.407424612
##  [53,] -0.906545994  1.108874215  1.03521271  0.179671277 -0.804835301
##  [54,] -1.669956979  0.706463198  0.54089194  0.336371630 -0.952496542
##  [55,]  0.195017025 -0.473764877  0.02002028 -0.520758210  2.360776695
##  [56,]  0.200650077  2.716951889  1.41770341 -0.952121471  0.740632192
##  [57,]  0.518073225 -1.367268061  2.81032243 -0.783212228 -0.937364905
##  [58,] -1.831824121  1.109402015 -0.45190838 -0.415424258  1.192288451
##  [59,]  0.685756178 -0.408794213  0.31395717  0.052650501 -0.299515433
##  [60,] -0.498748639  0.460812608  0.14593215  1.348117096 -1.331297016
##  [61,] -0.851501742  1.873535014  1.07688266  1.057769336  1.654911975
##  [62,]  1.671406217 -0.423441611  0.01975544 -0.908557402  0.637102625
##  [63,] -1.102287719  0.573598828  1.07737079  0.769959205  1.589212310
##  [64,]  0.487489582  1.589885359 -0.52386479 -1.031169208  2.329019058
##  [65,] -1.821523333  0.607204567  2.39323915  0.916516254  0.021873142
##  [66,]  1.890194887  0.314196298  0.21915753  1.943292140  0.447955709
##  [67,] -0.908993115 -1.002601881  2.42194180 -0.792706294  0.098085784
##  [68,] -2.188253111 -1.295291142 -0.20414494  0.389988620 -0.418881441
##  [69,]  1.922127515 -0.483661450 -0.89450174  1.892882896 -0.799898913
##  [70,]  1.831473258 -1.208432390  0.77153641  2.788481409  0.126999960
##  [71,]  1.111645609  2.745232439 -1.90160470  0.587416793 -0.459646651
##  [72,]  1.972055116 -0.866834386  1.97362887  1.622670501 -1.020641169
##  [73,] -3.014541351  0.230927487  1.82358730 -0.870777134  0.323242135
##  [74,]  0.297544932 -3.341535872 -2.66498436 -0.870757883  0.580788533
##  [75,] -3.123513629 -0.202316474  0.02439536  0.353201837 -1.241766589
##  [76,] -2.175119346  0.619405502 -1.87693522 -0.203685676  0.728913726
##  [77,]  0.988165063  0.281111344  2.73257900  1.428695160  0.826564602
##  [78,] -3.171148404 -0.393624263 -0.52860137  0.462431181 -1.108134631
##  [79,]  1.909872378  2.594516335 -1.37039805 -0.316273317 -0.384527514
##  [80,]  1.884232732 -0.836929091  0.25971121  2.107873428 -1.134661282
##  [81,]  0.148410514 -2.759622666  0.17058795 -2.012337053 -0.253735238
##  [82,]  3.159260208 -1.376912455 -0.46218545 -0.031919056 -0.631448204
##  [83,]  1.589202745  3.215922052  1.45544104 -1.156249670 -0.416540691
##  [84,] -0.735262114 -0.558683606  0.06426583 -0.614419304  3.046112719
##  [85,] -2.492696658 -0.248148077  0.57351965 -1.485832190 -0.156211037
##  [86,]  0.164831585  1.067984585  0.76191427  0.778873264 -0.004490012
##  [87,] -0.791080564  1.277284906  0.13896203 -0.512508540  0.424119906
##  [88,]  1.019972886  1.038546046  0.67879987  0.166896049 -1.036950670
##  [89,]  1.355490521  1.048191345 -1.19753355 -1.835391137  0.487381401
##  [90,] -0.217694604  1.268039722  0.47349157 -1.166491895 -0.149140965
##  [91,]  0.200980870  1.569364821  0.23589533 -1.010042731  0.739065292
##  [92,] -1.224091912 -1.370670443  1.95314352 -1.673818763  0.298939223
##  [93,] -1.377079915  1.986294419  0.87166613 -2.146700312 -1.490469516
##  [94,]  1.105509567  1.009068862  0.89835083  0.952703555  1.771596512
##  [95,] -1.763739245  0.521690848  0.52910283 -1.278362192 -1.910301720
##  [96,]  2.144246653  1.031814241  0.70297021 -0.327085070 -1.299959938
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##  [98,] -0.943580309 -0.985801589 -2.47162486  0.257887623  0.377111320
##  [99,]  1.434728986  0.425244821  0.30490166  1.146598321  0.613218154
## [100,] -3.084789560 -0.318539996 -0.37773171  0.447133452 -1.342039635
## [101,] -2.211988131  0.291466382 -3.00610005  0.509360032  1.226245309
## [102,]  0.934186102  0.103006060  2.09662512  2.008597406  1.345721614
## [103,] -3.134406710 -0.118005299  0.30107545  0.285470960 -1.220197353
## [104,]  1.829037095  2.049999607 -3.14856312  0.573307112  0.274730687
## [105,]  1.889637650 -0.929392727 -0.06656941  2.287498244 -1.058126770
## [106,]  0.304495611 -2.796890852 -0.22372072 -2.193562275  0.775896724
## [107,]  3.150251750 -1.266687571 -0.15055069  0.047749838 -0.490198468
## [108,]  1.504721972  2.576287720 -0.70174306  0.107804727  0.494154681
## [109,] -0.513569276 -0.429919365  0.66685573 -2.146489489  1.272448570
## [110,] -2.049787993 -0.595265518 -1.39788656 -1.626354625  0.259757990
## [111,] -0.548863117  0.551657627  0.36348773  1.955891473 -0.754455175
## [112,]  0.137370850  1.157565543 -0.22654103  0.220013284 -2.581582640
## [113,] -0.769133382 -1.651851800  2.04076114  0.144667909  0.027932525
## [114,]  1.052948611  1.877461485 -3.18476295  0.436016597 -0.942808927
## [115,] -0.832893079 -1.520043078  1.23238975  0.789310913  1.071200271
## [116,] -0.521560718 -1.774839073  1.77212639  0.062067842  1.766517195
## [117,] -2.590558669 -0.606042808  0.07011790  0.065104794 -1.677476972
## [118,]  2.565856126 -0.636635561  0.90085819 -0.352743399 -1.971483866
## [119,]  1.890132650 -1.553285458 -0.21632974  2.489127348 -0.444483208
## [120,]  1.809485293  2.507239709  0.23379629 -0.904604737 -0.130106958
## [121,]  1.154753405 -0.820601807 -0.18191235  3.258811319 -0.010433839
## [122,] -3.068643554 -0.358110282 -0.17957410  0.278724442  1.079820384
## [123,]  0.603092803 -1.663570228 -0.81847194 -1.742527977 -1.373236514
## [124,] -0.262265717 -0.458918399  1.14583763  0.431171055  0.242487727
## [125,] -2.166676433  1.025027556 -2.44144452 -0.175700086  0.158619707
## [126,]  1.396820173 -1.775823130  0.44315452  0.164190546  1.111925399
## [127,] -2.621538470 -1.080128160 -1.50955976  0.829755886 -1.228986208
## [128,]  1.904628487  2.458422492 -1.72758409 -0.464085245 -0.547767196
## [129,]  2.449232521 -1.233115913  1.14940570  0.807738005 -1.464755784
## [130,]  0.346806820 -2.486510669  0.79296731 -2.700072211  0.411814347
## [131,]  3.029389183 -1.278867895  0.12853282  0.002537778 -1.822456522
## [132,]  1.929414827  1.312693320  1.78007480  0.409498610  0.912824308
## [133,] -0.087138867 -2.322217437 -0.65856528 -1.925296028 -0.156916374
## [134,] -3.286936885 -0.510578871 -1.06794608  1.550312925  0.014328320
## [135,] -0.243063096  3.265766261  0.36303718  0.455074271 -0.101216908
## [136,] -0.885383059 -0.103152291  0.79354384  1.149680047  0.191778725
## [137,]  0.779845934 -1.412199847 -1.48333758  0.232939883 -1.659993771
## [138,] -1.475619881 -1.358995678  0.78667103  0.785254199  0.063938933
## [139,]  1.315156524  1.874152974  1.90819130 -1.745565666 -2.120481240
## [140,] -1.435594309 -0.886655409  1.17170443  0.402456719  0.175080477
## [141,]  0.311554205 -1.503514600  1.98669876 -0.611745934 -0.377702324
## [142,] -1.898169897 -0.689807691 -1.77090536  1.813131302 -0.926438974
## [143,]  1.817982682 -0.274894663 -0.25700981  0.816135845 -1.374023354
## [144,]  1.132188201  0.097406071  1.56257454  1.507813279 -0.597525384
## [145,]  1.041211639  2.476633973 -2.22422610  0.853838815  0.789743107
## [146,]  1.911956582 -1.279682355  0.58493540  2.442926394 -0.412810097
## [147,] -2.208254898  0.244829063  1.39493556 -0.446948312 -0.084142771
## [148,]  0.199618587 -1.606668229 -0.56648477  0.211079060  1.819639955
## [149,] -3.151824202 -0.105442765  0.28680901  0.530946496 -0.974148171
## [150,] -2.581152399  1.660530129 -0.45658460 -0.913041511 -0.642489672
## [151,] -1.821212050  0.049106818 -0.42528735  0.326193983 -1.727503000
## [152,] -0.709027954  1.118219938  0.61257539 -0.562639222  0.859330817
## [153,]  1.527353442 -0.054701131 -0.07747901  0.328574008  2.559335815
## [154,]  0.134446169  0.264009802 -1.70348774 -1.428607876 -0.536373103
## [155,]  2.379419131 -0.094554298  0.55507534 -2.767771658  0.132335453
## [156,]  1.816004356  0.546117886 -3.21264766  0.454846344  0.862978356
## [157,]  0.693446059  0.977045613  0.26008812 -3.763916185 -2.021635959
## [158,]  1.637082331 -0.335000397 -2.05755169 -0.746108139 -0.416159349
## [159,]  0.296933463  1.194165867  2.60436670 -1.181630957 -0.546751798
## [160,]  0.822754284  0.670235764 -2.41335728 -1.103663683  2.312033587
## [161,] -0.918911402  0.663806963  1.18690797 -2.128116926  1.024959096
## [162,]  0.231900961 -1.270641543 -1.76967126  0.862961366  0.236368161
## [163,] -1.013939681  1.262821648  1.47304856  0.585206501 -0.098566521
## [164,] -1.772694007  0.767271176  0.63712578  0.973149028 -0.128283972
## [165,]  0.113097963 -0.357041885  0.30262585 -0.029388012  3.038456413
## [166,]  0.075576812  2.276081375 -0.14913244  0.428758735  1.958389064
## [167,]  0.477358107 -2.002383447  0.60892730  0.553159679 -0.100163895
## [168,] -1.789229364  1.010323518 -0.71414648 -0.663628669  0.826928708
## [169,]  0.719595969 -0.266957041  0.81937861 -0.376044152 -0.660229054
## [170,] -0.479345237  0.029424455 -1.25225042  1.746517856 -1.293222426
## [171,] -0.706487604  1.979788355  1.48164274  0.256635741  0.659195101
## [172,]  1.659264316 -0.669984273 -0.80889570 -0.497190062  0.868951875
## [173,] -1.053631487  0.418816948  0.64807542  0.512000760  1.171296835
## [174,]  0.439619994  1.347267284 -1.34471999 -0.491319346  2.768031869
## [175,] -1.736485551  0.889505297  3.31946123  0.301066951 -0.567055601
## [176,]  1.908193822  0.100984757 -0.40588659  1.869485714  0.234457926
## [177,] -1.025193951 -1.347023632  1.14815308  0.528994073  1.290656942
## [178,] -2.229264288 -1.622311063 -1.29643165  0.990124308  0.004899612
## [179,]  1.957225328 -0.433792361 -0.55469125  1.069085426 -1.511190662
## [180,]  1.838526733 -1.356872831  0.31115872  2.847776221  0.079447061
## [181,]  1.180112751  2.940457687 -1.22406253 -0.005852669 -1.024121550
## [182,]  1.811861750 -1.441142807  0.01690577  3.101211177  0.312426585
## [183,] -3.110670459 -0.364952154 -0.24358794  0.575227017  1.429197339
## [184,]  0.360229263 -2.696506149 -0.58357746 -1.726264724  0.050562343
## [185,] -3.223541067 -0.179218190  0.09257126  0.673772079 -0.685860956
## [186,] -2.269746579  0.759892939 -1.50517585  0.258232091  1.433596248
## [187,]  2.747577269 -0.892695063  0.37334010 -0.956311448  1.532003894
## [188,] -0.149697264 -1.642331214 -2.28814301 -1.471419303 -0.781235965
## [189,]  2.400777592  0.347128955 -1.71026348 -1.021489585  0.434261725
## [190,]  2.664155409 -1.393549647 -1.71837991  0.529051941  0.057805594
## [191,]  0.613534144 -1.458382780  0.89659577 -3.179203564  1.045150296
## [192,]  2.833005133 -1.403952109 -1.83872171 -0.412027674  0.480801518
## [193,]  3.117056920 -0.179410694 -1.10177848 -1.856855416  0.106854315
## [194,]  1.396552964 -0.642255545  0.02050933 -3.110585372  1.836705087
## [195,] -2.512642306  0.003850388  1.41044718 -1.765460899 -0.188561541
## [196,]  0.041302770  0.619388750 -0.80700898  2.078283851  1.142567875
## [197,] -0.813244847  0.880928753 -1.22887662  0.288977960  0.912007999
## [198,]  0.986709032  0.840164793  0.05264538  0.423153898 -0.837258657
## [199,]  1.252252204  0.988451934 -1.42301728 -1.323117294  1.159512551
## [200,] -0.137885258  1.481731866  1.13219939 -1.525196202 -0.559153131
## [201,]  0.136542296  1.207505130 -0.99116369 -0.216929658  1.363785406
## [202,] -1.270419897 -2.048452421 -0.26872446 -0.709046147  0.847964695
## [203,] -1.511779573  1.885698680  0.38947345 -1.030942437 -0.282150752
## [204,]  1.085397022  1.243127916  1.68487628  0.664169343  1.724253118
## [205,] -1.937338444  0.418609362 -0.03359575  0.232284332 -0.284578291
## [206,]  2.079880884  0.956433882  0.49279972 -0.166467991 -1.020841607
## [207,] -0.238660237  0.398472349 -1.03260961  0.864147837 -0.508793937
## [208,] -0.159651843 -1.132594137 -0.05598138 -1.013129749 -0.784261739
## [209,]  1.500566250  0.840189583  1.66536450  0.435082161  0.072426854
## [210,] -3.014209221  0.355964728  1.96591223 -1.080854377 -2.396209206
## [211,] -2.105058072  0.929924423 -0.80062808 -1.017803085  0.046453380
## [212,]  0.942418911  0.054526904  1.96648773  1.934291974  1.240767541
## [213,] -3.148924082 -0.594610120 -1.31041545  1.087399067 -0.793683557
## [214,]  1.878394695  2.398574133 -1.99024350 -0.062447648 -0.190863682
## [215,]  1.966715740 -0.630957885  1.05402026  1.155588169 -2.010604775
## [216,]  0.277041266 -2.759604202 -0.07945444 -2.231880620  0.846800791
## [217,]  3.171498795 -0.995402267  0.71278740 -0.251134699 -0.651266456
## [218,]  1.556928786  2.591469129 -0.66355483 -0.035006615  0.235938143
## [219,] -0.616500433 -0.513737474  0.21506585 -1.061891800  2.369939157
## [220,] -2.586211894 -0.187369377  0.72652260 -1.088595931  0.457090666
## [221,]  0.137716815  0.366509534 -0.16792988  0.543739987  0.849702117
## [222,]  0.865093182  0.844185218 -1.74842823 -1.798595288  1.737694179
## [223,] -0.913971012  0.969266395  1.97298215 -1.716775781  1.472684147
## [224,]  0.313977949 -0.945041768 -0.72531396  0.292773295 -0.288118442
## [225,] -1.072776501  0.599121897 -0.68085976  1.492600012  0.450812463
## [226,] -1.699472023  0.930082069  1.24714633  0.260609994 -0.813935347
## [227,]  0.251825578 -0.075337937  1.19428496 -0.695732642  2.249570554
## [228,]  0.014567830  2.117497330 -0.74689429  1.102971967  2.580198736
## [229,]  0.504752774 -1.860630264  1.15079860  0.009577708 -0.529532914
## [230,] -1.698692239  1.131623356 -0.33312414 -1.038468810  0.327760281
## [231,]  0.558690456 -0.191830970  0.83866091  0.887454211  0.824592143
## [232,] -0.464475998  0.564705610  0.54205784  0.907998903 -1.720403026
## [233,] -0.736607022  2.290777684  2.53098650 -0.131746814  0.602622034
## [234,]  1.791907070 -0.482831255 -0.20730594 -1.103593125  0.098407869
## [235,] -1.021622690  1.026768352  2.49920628  0.201024453  1.131623848
## [236,]  0.511871527  1.643341139 -0.30949731 -1.318210021  2.062253193
## [237,] -1.857682768  0.067118102  0.65282615  1.571807247  0.370261802
## [238,]  1.973432877  0.329461293  0.39577264  1.190688519 -0.369711578
## [239,] -0.844025398 -1.043350556  2.43615654 -1.497678287 -0.655538378
## [240,]  1.798603632  1.277822318  1.64041006  0.964305961  1.712072698
## [241,]  0.567970913 -1.465901428 -1.40821954 -1.475588124  1.328585265
## [242,] -3.128591618 -0.100406746  0.42598650 -0.002631206 -1.449540091
## [243,]  0.921300172  2.566347959  0.08444693 -0.327261230 -0.277565465
## [244,] -0.707766669 -0.140351712  0.50896513  0.494931879  0.794661098
## [245,]  0.727027732 -1.433071548 -1.59685113  0.593875654 -1.235796634
## [246,] -0.813209418 -1.199505257  0.40464481 -0.405256608 -0.735537650
## [247,]  1.137562086  1.419593842  0.28112686 -0.123186538 -0.567331492
## [248,] -1.568549443 -1.353854798 -0.38152350  1.471266594  1.164907662
## [249,]  0.206337661 -1.720761209  1.11360977  0.581416058  0.745153770
## [250,]  0.582400965 -1.654341741 -4.03720871  0.592072897  0.127026158
## [251,]  1.852485410  0.064395647  0.86057895  0.277190722 -1.725563610
## [252,]  1.069824793  0.099379354  1.64192217  1.436102237 -0.464752520
## [253,]  1.320083419  3.019301770 -0.60379759 -0.838972788  0.575723760
## [254,]  1.826416008 -1.528447714 -0.21991298  2.977344774  0.131843922
## [255,] -2.295131492  0.231836563  1.14798587  0.601866665  0.972169398
## [256,]  0.184324517 -1.188753076  0.66614989  0.264048756  2.108122913
## [257,] -3.143108851 -0.334761125 -0.41121557  0.580820285 -1.073009725
## [258,] -2.658851944  1.282851605 -1.79186198  0.149784893  0.220653288
## [259,] -1.871308247 -0.027948405 -0.67512508  0.569331753 -1.428769300
## [260,] -0.711591973  0.787827363 -0.51712533  0.015709149  1.149714717
## [261,]  1.686997211  0.200537154  0.82927435 -0.749102450  1.380292709
## [262,] -1.858110215 -0.038377392 -0.44768335 -0.780682656 -2.102146836
## [263,] -0.009983675 -1.961070989 -0.67218900  0.977524185  1.756913624
## [264,] -0.640492349 -2.449177339 -0.47626302  1.394993461  2.816254162
## [265,] -2.667743902 -0.624537600 -0.07078989  0.631216256 -1.022190383
## [266,]  2.455060778 -0.932060495 -0.13446506  0.605103847 -1.049802875
## [267,]  1.289042304 -1.784059560 -2.00134352 -1.157706179 -0.679250082
## [268,]  1.464834078  3.334018842 -0.17613207 -1.228668742 -0.968154666
## [269,]  2.198079582 -0.920094403  1.60613778  0.943922005 -0.588805903
## [270,] -2.876746306  0.339743512  2.19185099 -1.486040419 -0.507401063
## [271,]  0.060055521 -3.317302160 -2.37218122 -0.195895671  0.166259201
## [272,] -3.142504794 -0.257942521 -0.17738398  0.552812520 -1.059087544
## [273,] -2.634807935  1.168554355 -2.23638980  0.468363114  0.337151628
## [274,]  1.505301199 -0.740318106  1.46628345  1.427782791  1.331421460
## [275,] -2.740709424  0.722367627 -0.45692349 -0.908981952 -0.263057377
## [276,]  1.905774831  2.562920015 -1.43666755 -0.402881750 -0.453816513
## [277,]  2.017633169 -1.986659604  0.38967132  0.286357120 -0.144177349
## [278,]  0.099735552 -2.950607582 -0.86988372 -0.826878661  2.360250992
## [279,]  3.015656624 -1.371646389 -0.56504871  0.865577325  0.487728246
## [280,]  1.825438683  0.837995677  0.24336244  1.242694873  1.631988024
## [281,] -0.131569292 -2.296085695 -0.47529079 -2.174913004 -0.202269462
## [282,] -1.322834911 -1.037008743 -0.41131805 -1.699174863 -2.575108219
## [283,]  1.736775731  1.283284999 -1.49919175 -0.917952163 -1.119800076
## [284,] -0.592930367  0.224645288 -0.78024226  2.755903856 -0.168581495
## [285,]  1.928894090  2.708029329 -0.86288820 -1.014020749 -0.920456081
## [286,]  2.367428208 -1.947699135 -1.30903111  2.358687696 -0.378804689
## [287,]  0.290098251 -2.530916123  0.71152818 -2.701725928  0.558829150
## [288,]  3.070879292 -0.884056499  1.49195594 -0.861410776 -2.416739566
## [289,]  1.901858849  1.316866466  1.83316729  0.347207053  0.949670177
## [290,] -0.148458186 -2.510569491 -1.25163372 -1.591987828  0.190570397
## [291,] -3.160670480 -0.142895407  0.08071687  0.912125001 -0.674116273
## [292,] -0.350752444  2.762553158 -1.29900566  1.452158009  0.740670485
## [293,] -0.898366238 -0.174979956  0.55300720  1.296536856  0.308268936
## [294,]  0.861502720 -1.425901982 -1.64547390  0.420718507 -1.767384879
## [295,] -1.473211209 -1.294127913  1.01677328  0.634936076 -0.026911060
## [296,]  1.111453285  0.841309250 -1.52709178  0.333852745 -0.419205639
## [297,] -1.529405423 -1.178528936  0.25100317  0.921255092  0.711687244
## [298,]  0.258107397 -1.743891382  1.19553857 -0.139263124  0.027543069
## [299,] -1.904656129 -0.528637935 -1.18196439  1.415971336 -1.132951811
## [300,]  1.848956846  0.029663156  0.79616089  0.147726816 -1.830864913
## [301,]  1.150509115  0.284559833  2.21074344  1.095715426 -0.877160551
## [302,]  1.152918867  3.108695777 -0.10406543 -0.443281716 -0.231421332
## [303,]  1.932277477 -1.124180447  1.11643983  2.110205036 -0.653007261
## [304,] -2.222289178  0.217516381  1.31604101 -0.408380875 -0.025831892
## [305,]  0.309135098 -1.125563191  1.01347625 -0.729745122  1.004636281
## [306,] -3.290318919 -0.773981843 -1.92760392  1.864300336  0.137285445
## [307,] -2.664442991  1.297484746 -1.64793851 -0.204320402 -0.026482672
## [308,] -1.831829290  0.042083823 -0.43588975  0.322802182 -1.701712188
## [309,] -0.648431973  1.114788359  0.51649880 -0.439377745  0.770588458
##                  PC6           PC7          PC8          PC9          PC10
##   [1,]  0.7182594090  0.0900371245  1.051744451 -1.937650817  0.4989633841
##   [2,] -0.6772550951  1.9777064114 -1.557168739 -1.216866754 -0.5305604825
##   [3,]  1.1916488129 -1.2195053227 -0.411285727 -0.323523971 -0.1148162874
##   [4,]  1.7403584683  0.6091639642  0.258612735 -0.654105790 -0.2130147794
##   [5,]  2.1847893962  0.2198466952  1.845426766  0.627204075 -0.6014890431
##   [6,] -0.2480383908  1.4550678660  0.483870124  0.558138013 -0.2014692509
##   [7,]  0.9965416546 -0.8530147261  0.684045214 -0.285018564 -0.7811912336
##   [8,] -0.5055130553 -0.4251606584 -0.227317424  1.333349131  0.1917601304
##   [9,]  1.1709683751  0.1970313925 -1.162926497  0.312410711 -1.0231229714
##  [10,] -1.4206369931 -0.3235588013  0.045516341  0.241215288  1.0354175725
##  [11,] -0.9877439635 -0.2335341620  0.675723070 -0.141706192 -1.1092713774
##  [12,] -0.7610221388  0.7783351846 -0.103927236 -0.972945187  0.3836599781
##  [13,]  0.7356356660 -0.1182467785 -0.538078442  0.115259335 -0.8498243779
##  [14,] -0.3303380494 -0.4144204301  0.078712304  0.509575391 -0.1786395470
##  [15,]  0.8668959754  0.1542886143 -0.441232526  1.201097550 -0.7763798784
##  [16,] -1.0582597188 -0.7242179155  1.600738198  0.810017235  0.0978269150
##  [17,] -0.5049244711  1.7816022095 -0.061502145  0.001210227 -0.9101287848
##  [18,]  0.1840838476 -0.0442652608 -0.003095435 -0.819714203  0.2257921571
##  [19,]  0.4184360878  1.5182832851 -0.362960279  0.678886989 -0.0700320345
##  [20,] -0.1026575213  0.1029842000  0.139143879 -1.173656688  0.0186207447
##  [21,] -1.1480175988 -0.8296570774  0.839375250 -0.234943802 -0.0825857254
##  [22,]  1.3263081293 -0.4222197926  0.444424752  1.718445639 -0.4170879515
##  [23,] -3.4638911787 -2.6363622952  2.172674109  1.263816491  0.8334590948
##  [24,] -0.0004180954 -0.1158383494 -0.076506354  0.541266927 -0.3670905070
##  [25,] -0.2750442777  0.9287661421 -0.325823814  0.423680522 -0.5182746874
##  [26,]  1.0816548676  0.0640144973  1.274308400 -1.764172546  0.3344585771
##  [27,] -0.2832546918  1.2360719838 -0.187090224  0.315365054 -0.0554968227
##  [28,]  1.3433206731 -0.8591849926 -0.936163793 -1.220062630  0.4830794498
##  [29,] -1.6799924024 -0.0281633721  2.156630368 -1.020784884 -1.1447949606
##  [30,]  1.0710626285 -1.3284110672  1.834728862 -0.381994526  0.6811806747
##  [31,]  0.8185042829  0.1595997123  0.965113863  0.982824838 -0.1867421466
##  [32,] -0.5116245789  0.2213173362  0.411993823 -0.538385421 -1.0926900877
##  [33,]  1.2290071541  0.4714686091  1.461225803 -0.325889829 -0.2473663898
##  [34,] -0.0646666045  2.2433620737  0.710404490 -0.950511191 -0.7809675133
##  [35,]  2.4754853111  0.2893439181  0.923999043 -0.982576123  0.6579637222
##  [36,] -0.1422025234  1.3713987956  1.491799348 -0.266482715 -1.0176272530
##  [37,]  0.8160953361  0.5636397794  2.230793234 -1.029467745  0.4891853321
##  [38,] -0.3534221454 -0.7417774978  1.638132555 -1.319142919 -1.6484147935
##  [39,] -0.1721706898  0.0335387929  1.024852681 -1.148675650 -1.2064988678
##  [40,] -1.1755253233 -0.3055779800  0.531840085  0.641114542 -0.3585174104
##  [41,]  0.3339185093  1.5334741172 -0.742220999  0.397824082  0.6322714144
##  [42,]  0.1743686979 -2.4061791305 -1.430371076 -0.412504818 -0.2390151804
##  [43,]  1.0164937988  0.2833156337 -0.990443898 -0.608638156 -0.8755992881
##  [44,] -0.6089020677 -1.6271801419 -0.979063296  0.261435435 -0.0709340761
##  [45,] -0.2960954667 -0.0609937498 -0.506122202  0.560648901 -0.3045133671
##  [46,] -0.4779798997  0.7123433988 -0.252310393 -1.474850571 -0.4690179776
##  [47,] -0.5681313101  1.8002197935  0.989506417  0.151660074  0.5940115661
##  [48,]  0.0650024003 -1.6861801155 -0.882564748  0.225197238 -0.6288864935
##  [49,] -1.3100505736  0.3797064291 -1.171015537 -1.344665437 -0.7421368508
##  [50,]  1.3420468766 -0.3811321637 -0.227571574 -0.652518402  0.3433578516
##  [51,] -0.8400332772 -1.4635314100 -1.078142846  0.099897456 -0.1895171928
##  [52,] -0.8236403909  1.1294305256  0.840477295  0.190213575 -0.6073655522
##  [53,] -0.7293181061 -2.1049759827 -1.159698724  1.358785707 -0.9020524475
##  [54,] -2.3456226474 -1.5198752771  0.052128540 -0.129470207 -0.1026399486
##  [55,] -0.8361005036 -0.9337361769 -0.234221327  1.426062323  1.7765311821
##  [56,]  0.6763606802  0.0390138240  2.563417845  0.722616967 -0.3790244685
##  [57,]  1.6946080427  0.0698616819 -0.534759032  0.043136450  1.5033693120
##  [58,] -0.3582806110  1.6811886957  0.042283265 -1.182450667  0.7849571961
##  [59,] -1.3495183401 -2.2578695319  1.090262317 -2.250237313  1.0030432414
##  [60,]  0.2690629341  1.1554971565 -1.160881822  0.832217716  1.6653117813
##  [61,] -0.7234518984 -0.6127871702 -0.742339680 -0.649836684  0.8693699595
##  [62,]  2.7376481997  0.5069278238  1.443017228  1.237888114  0.4514609616
##  [63,]  1.4658335990 -0.9257069648 -0.898460096  1.182587630  0.7225827545
##  [64,] -0.3455726719  0.3440809009  0.421923404 -0.198799051 -1.7624832578
##  [65,]  1.0291862289  0.3015066007 -0.973691647  0.197857462  1.1499283042
##  [66,] -0.8641232698 -0.0765569415 -0.652176582 -0.405376799 -0.8177445459
##  [67,] -0.8224879637  0.4260268121  1.467835590  0.414959404  0.5598897961
##  [68,]  1.4683182389 -0.1736121977  0.029019490 -0.125692739 -1.4472406140
##  [69,] -1.1647333718  1.0018628504 -2.021014782  0.026036013  0.7065863902
##  [70,]  0.7122713714  0.4831732842 -0.770951147  0.048311261 -1.3917275625
##  [71,]  0.2163691129  0.2332136225 -1.264055897  0.342708666  0.8105451156
##  [72,]  0.8927285143 -0.0892148898 -0.031393992  0.512702951 -1.4173886846
##  [73,] -0.1471944405  0.8343504360  0.160820099 -0.725256307  0.0941240714
##  [74,] -1.2948417212 -0.0557786798 -0.137358569 -0.634600071 -0.5015041758
##  [75,] -0.0085485247 -0.0638697694 -0.138921766  0.508917015 -0.3690218531
##  [76,]  0.8865859209 -0.8394523284  0.524187877  1.924133725 -1.0392422670
##  [77,] -0.9823598934  1.2710772242 -0.440050417 -0.551349005  0.2165906641
##  [78,] -0.3369973922 -0.5403419775  0.209784606  0.463483093 -0.1534376132
##  [79,]  0.0259121267  0.4476842656 -0.627700825 -0.986909443  0.2319467291
##  [80,]  0.2603971391  0.8509880060 -1.147268964 -0.332077475  0.4277897576
##  [81,]  1.3454849598 -0.4571683277 -0.020774310 -0.503014456  0.0002491504
##  [82,] -1.3530858031 -0.3732312052  0.223143075 -0.520275980 -0.0422490303
##  [83,] -0.7627017522  0.3161724869 -0.237643091  0.721497336 -1.3314564476
##  [84,] -0.0620643948  1.6063796501 -1.349044882  0.595672201  0.4284075233
##  [85,] -0.6206514250  0.4762684616  0.434017829 -0.448693689  1.6330839047
##  [86,]  2.1908847748  0.1637682633  2.454547104 -0.535495194 -0.5434528668
##  [87,]  0.2751173563  2.4020282519  1.387369642 -0.084458879  1.8146097334
##  [88,]  1.6504616104 -0.6662903002  0.575775492 -1.644130385 -0.1523657271
##  [89,] -0.2146076649  1.4666407787  0.505539732  1.817924110 -0.4343689651
##  [90,] -2.1768553940 -1.7351397721 -1.333156393  0.080157982 -1.2516603384
##  [91,]  1.0186361905 -2.0232826855 -0.799342765 -0.912119506 -1.0274541464
##  [92,] -0.2200662088  1.8899057953 -0.629502096 -0.091212678  0.6710501797
##  [93,] -1.0107223981 -0.8968021944 -0.126530551 -0.421850393 -1.4183187612
##  [94,] -1.1577149024 -0.0636793450  1.564665414  0.807153497 -0.0043867516
##  [95,] -1.5072647311  0.0592587589  0.582670492 -0.164119150  0.3775130916
##  [96,]  1.5259187055 -0.9655011371 -0.748051421 -1.302623761  1.4527806508
##  [97,] -0.1637854681  1.5368529740  0.950410816  1.721597416  0.9008138964
##  [98,]  0.9508989263 -0.8494160616 -0.248636294  0.471625838  0.4169054384
##  [99,]  1.0144025218 -0.4992410790 -0.560620283  0.691692676  1.7044333766
## [100,] -0.3562594091 -0.5342511547  0.203608313  0.652327066 -0.1601264925
## [101,]  0.3708067531 -1.1246810404  0.567242964  1.835325079 -0.7690079514
## [102,] -1.1290063766  1.4719086875 -0.743095409 -0.735893847  0.2628648726
## [103,]  0.2041381246  0.2229040775 -0.345847951  0.449964713 -0.4987912831
## [104,] -0.8695346006 -0.3409421701 -0.232314140 -1.113917852  0.7431986222
## [105,]  0.0723947812  0.6925719895 -1.069418071 -0.310371025  0.5304621119
## [106,] -0.0554569866  0.0755250438  0.196947992 -1.101256206 -0.0028281165
## [107,] -1.0389338753  0.2008116952 -0.247093174 -0.624737779 -0.2552554493
## [108,] -1.7760017934 -0.3625785345 -0.024329847  0.546246507 -0.7826981967
## [109,] -0.6959887781 -0.5506915739  0.722714406  1.481103955  0.9582937953
## [110,] -1.5009075090 -0.2694747464  0.242771907 -1.313300537  1.7446768220
## [111,]  0.7721592121 -0.5007936668  1.741059639 -1.582473312  0.5383504753
## [112,] -0.1786876761  1.0043210869 -0.076456082 -0.295559463  0.6303679021
## [113,]  1.0975871227 -0.7515649166 -0.976754994 -0.483134189 -0.1330556079
## [114,]  0.8109343836 -0.0744906829  0.525611419 -0.724544164  0.2928001118
## [115,]  1.6989983193  0.2889697648  0.580747364  0.065922053 -0.5144149776
## [116,] -0.2374686197  1.2887322457  0.673565647  0.620826656 -0.1856408041
## [117,]  0.8656125423 -0.6423756808  0.379169440 -0.454051005 -0.7442702200
## [118,] -0.5384903355 -0.4441595600 -0.224210212  1.318922104  0.2098020718
## [119,] -0.3552300797 -1.4745007896  0.838083505  0.467445375 -0.6716257921
## [120,]  0.3387541618 -0.6407139977 -0.198961684  0.689511369  1.2276216679
## [121,]  0.9136912900  0.2426837929 -0.602595371 -0.581945067 -0.7445689248
## [122,] -1.1391646868  0.1148555047  0.433621924 -0.820832543  0.6339637929
## [123,]  0.1651649186  0.7809959958  0.376483824 -0.884545536 -0.5064679539
## [124,] -0.7451062410  1.6588536662  0.946834768  1.341799538 -1.1139316268
## [125,]  0.8235605948  0.7164128606 -0.963286338  1.235061630  0.4581502578
## [126,] -1.2672067972 -0.0068735808  0.836256857  1.088810772  2.0241027825
## [127,] -0.0077115597 -1.4676015751  0.832255495 -0.458713706 -0.2460666886
## [128,] -0.3383763662 -0.2722116474 -0.024674611 -0.888835497  0.4888132531
## [129,]  0.7419381633 -0.1076489376  0.029390947  0.658058499 -0.0578570215
## [130,]  0.4638030230  0.5378067703 -0.038345799 -1.038889873 -0.2992065070
## [131,]  0.0945553526 -0.9337798477  0.063322004  0.148915534 -0.0602388136
## [132,]  1.2095806065 -0.6453998127  0.638445956  1.914751260 -0.3481466341
## [133,] -1.3843500914  0.8000989766 -0.537640722  0.703789691 -0.5316666565
## [134,] -0.0455328316  0.7556806541 -1.079006294 -0.041677733 -0.4355276635
## [135,]  0.0231238238  1.6988749691  0.703402459  0.445462885 -0.9924850506
## [136,]  1.7888091581  0.0585350854  0.594625140 -1.524956540 -1.0868101484
## [137,] -0.9717704657  0.6457854708  0.219401552  0.829861806  1.0510281059
## [138,]  1.1832826573 -1.0601524697 -0.796831970 -1.180393963  0.5788461576
## [139,] -0.0508669693  0.9429216129  1.951171888 -0.613932393 -2.0182766483
## [140,]  2.0870227677 -0.3011120027  1.238775379 -0.296857101  0.0855744387
## [141,] -1.4389026065 -0.8796265990  0.915326198  2.103435482 -0.2405369992
## [142,]  0.3051253884 -0.1952539981  0.443883211 -0.826697048 -0.4671736948
## [143,] -0.0369880082  0.3343112252 -1.030124644  0.345427832  0.6008144372
## [144,] -2.0400765567  0.5119759210  0.028013880  0.415284019 -0.3025763820
## [145,]  0.0930397639 -0.6174323406 -0.562455850 -0.263503826  2.0504662305
## [146,]  0.2528038411 -0.5038819253  0.087127034  0.383882144 -1.0715888920
## [147,] -0.8005831934 -0.1851281935  1.863196139 -0.131122830  1.2344499680
## [148,] -1.2396387560 -1.4756288359 -0.010519121 -1.086185872  0.6454765490
## [149,]  0.3454322958  0.6440632709 -0.738175847  0.337190365 -0.6142109170
## [150,]  1.0461288333 -0.3753863876  0.241411442  1.484269431 -0.7944864282
## [151,]  0.4209853126  1.5278721225 -0.687656836  0.474918495  0.5901247880
## [152,]  0.6397347854 -2.2017917867 -1.407752004 -0.261232284 -0.4801552665
## [153,]  0.2325984366 -0.3262884833 -0.732604948 -0.727790279 -0.4395895903
## [154,]  1.7338435668 -0.3562352562 -2.052488478 -0.296390537  0.0705721633
## [155,]  1.0210620303  0.3541803589 -0.677654700  1.131487179 -0.6532506045
## [156,] -0.0180242128  0.9453445750 -1.094053230 -0.793053986  0.9228261852
## [157,]  1.1350807495  0.1674140587  1.243957952  0.085922136  0.1750268486
## [158,]  0.4899893085 -1.1671787616 -0.681688653  0.926498219  0.7351731185
## [159,] -1.6011891275 -0.5675271901 -0.265382182 -0.912439898 -0.5072070942
## [160,]  0.8174613115 -0.2245479761 -0.686193244 -1.048232404  0.5737234783
## [161,] -1.1636492127 -1.7089218451 -0.983401957 -0.039235966 -0.0037856410
## [162,] -1.4764985239  0.7060534460  0.960802202  0.041287018 -0.2532281652
## [163,]  0.0123849297 -0.6225543814 -2.420133891  0.891850886 -1.4077121018
## [164,] -1.7770760442 -0.1299594593 -1.195363581 -0.588911094 -0.5208351046
## [165,] -0.2199517199  0.4277816483 -1.423403106  1.025766645  1.3378403183
## [166,]  0.2780319606  0.4388036958  1.903119075  0.301594364 -0.2373823573
## [167,]  0.6121603471 -0.6378332192 -0.319995207 -0.037338226  2.0790400840
## [168,] -0.7707938729  0.8283199021  0.772443060 -0.954741742  1.0728323789
## [169,] -1.2021527111 -2.3460650000  1.267380424 -2.135401657  0.9447027093
## [170,] -0.7205278287 -0.1291437145 -0.256494050  1.025728132  2.2676347800
## [171,] -1.0264924611 -1.6772936407  0.289434663 -0.132068480  1.1206742753
## [172,]  2.2782600232  0.0826961192  1.671016160  1.242534575  0.7115186472
## [173,]  0.8998145765 -2.0343515648  0.034489718  1.459591140  1.1109537286
## [174,] -0.6761343382  0.2146982763  0.387838889 -0.321613878 -1.5924299842
## [175,]  1.3497806076  0.3745604622 -0.878306889  0.414728710  0.9856275880
## [176,] -1.4501292141 -1.0857408632  0.157376686 -0.221442977 -0.4288626087
## [177,] -1.0214775390  1.1091632617  0.599886515 -0.021933204  0.5747927226
## [178,]  0.9320217107 -0.5867890683  0.201682913 -0.198283475 -1.1501934465
## [179,] -1.3591435209  0.0330178224 -1.051696479  0.291954748  0.9157083789
## [180,]  0.3486106719 -0.0599003018 -0.360551765  0.134912154 -1.1608604319
## [181,]  0.3677946878  0.0377246467 -0.962664974  0.559060480  0.7590612137
## [182,]  0.2758235097  0.0118436664 -0.480229844  0.049761629 -1.1341711040
## [183,] -0.9741297245  0.6021690226 -0.022182872 -0.999941633  0.5033614307
## [184,] -0.1010498318  1.2385747039 -0.937122001 -0.619518881 -1.2081725818
## [185,]  0.3706486873  0.7600695114 -0.861416151  0.154897374 -0.6289121694
## [186,]  1.5819467904  0.6204102094 -0.733805428  1.484436263 -1.5236970667
## [187,]  0.7652837924  0.4368488852 -1.076046923 -0.420415389  0.5967887802
## [188,]  1.2777193864 -1.2604820337 -0.557196949  0.016967831 -0.2540919744
## [189,]  0.8515111665  0.4899797137 -0.268220706  0.182423727  0.1965403010
## [190,]  0.7538761858 -0.4793833475 -1.430310635  0.854569132  0.1975468785
## [191,]  1.3256558842  0.4895357181 -0.900549936 -0.719720641 -0.6862211995
## [192,] -0.8281213472 -0.8545482639 -0.306147756  0.460734554  0.3932732045
## [193,]  0.1138488915 -0.4218965365  0.558712757  1.083030456 -0.0679257010
## [194,]  1.0918867660 -0.4414858098 -0.867641233 -0.154848657 -0.2057153022
## [195,] -0.0361418701  1.1940454863 -0.056101725 -0.572886618  1.2842161588
## [196,]  1.7467046384  0.4230309211  1.925306225 -0.928240235 -0.3631585981
## [197,] -0.4171954059  1.9082983690  1.570395017 -0.118208163  2.1876612889
## [198,]  1.3136000892 -1.0284662359  0.796197497 -1.683831453  0.0492111750
## [199,]  0.0235462607  2.2138935840 -0.205790580  1.454668455 -0.6216761071
## [200,] -1.9391008388 -1.5916732020 -1.358576237  0.258672413 -1.3882423287
## [201,]  0.5061086374 -2.2539731423 -0.817921519 -1.074066868 -0.7613814886
## [202,] -1.5006946642  0.5518371759  0.175508173 -0.071826492  1.4188995711
## [203,] -0.6275023585  0.5611925357 -1.548379259 -0.992608594 -1.7591623977
## [204,] -0.6194051296  0.5711016494  1.141953344  0.694678859 -0.3218729187
## [205,] -0.9273606014  2.1383255449 -1.425359927 -0.932253579 -0.1262317369
## [206,]  1.5353342036 -0.8566145090 -0.870725157 -1.469063084  1.4447359764
## [207,]  0.2843473182  2.3606655844  0.276786804  1.619469616  0.5927392689
## [208,]  2.1082846487  0.0794758735 -0.565386610  0.756200838 -0.1403342114
## [209,]  1.6773717584  0.0450418316 -0.809086210  0.807831385  1.3302258702
## [210,]  0.6991278108 -0.0095894399  0.179769365  0.836207202 -0.7043745674
## [211,]  1.2541072676 -0.8600370530  0.744939979  2.134547447 -1.2090722109
## [212,] -1.2882696167  1.1553962021 -0.476224826 -0.669127906  0.3736588436
## [213,] -0.7026680506 -0.6172392913  0.108360098  0.480835278  0.0133481689
## [214,] -0.3097785811  0.0864806846 -0.407527603 -1.022680111  0.4325845747
## [215,]  0.3030799705  0.1932021189 -0.391930040  0.002912519  0.4835420076
## [216,]  0.0884210532  0.2639798854  0.060627755 -1.184750704 -0.0865438470
## [217,] -0.5076065148  0.8397193769 -0.672936226 -0.646734882 -0.5770894616
## [218,] -1.9000416601 -0.6517011170  0.235922306  0.709875493 -0.6982881326
## [219,] -0.3537816061  0.8331990739 -0.634960319  0.992090639  0.6400768789
## [220,] -0.1420316905  1.5292124380 -0.488210514 -0.825313721  1.2978894992
## [221,] -2.7715548775 -1.1711189217 -0.224810404 -1.292249361  0.1126633235
## [222,]  0.9478196676 -0.5524772989 -0.253200914 -0.863825131  0.5535381578
## [223,] -0.3074748126  0.0308155105 -2.454120724 -0.296762847 -0.6126684205
## [224,] -1.0298320649  1.0206780718  0.855237899  0.215226261 -0.5046193620
## [225,] -1.2212535442 -1.9376653665 -1.617638308  0.884574081 -0.6814473948
## [226,] -1.7503323526 -0.6239726748 -0.629460887 -0.312870598 -0.4785053719
## [227,] -0.0392305174  0.2615016712 -1.130505607  1.396462056  1.2579694919
## [228,]  0.2225209433  0.8615858150  1.402180848  0.064659209 -0.2595934931
## [229,]  0.7412912740 -0.8531850969 -0.013240528  0.088707514  2.0467880852
## [230,] -0.7891935436  0.5454448937  1.084975113 -0.692704938  1.1037826112
## [231,] -0.2848528400  0.0915404055 -0.959288153 -2.908879872  0.2430427710
## [232,]  0.3190198692  0.8987541821 -0.848630395  0.972090818  1.6721437422
## [233,] -0.3048533945 -0.8294496564 -0.274188663 -0.289207469  0.6960047812
## [234,]  2.2580891391 -0.3672360792  2.171436426  1.635181116  0.7586462447
## [235,]  2.2292543596 -0.0922318122 -1.411306251  1.281549337  0.2631799499
## [236,] -0.3527796009  0.1126639646  0.675632513 -0.094287409 -1.7323666455
## [237,] -0.0255121956 -0.9127629007 -0.187010389  0.243044661  1.7805492648
## [238,] -1.2341259405 -1.2470149473  0.454072898 -0.011152504 -0.5126806365
## [239,] -1.2742061293 -0.8500378489  2.645838204  0.780696755  0.9179201758
## [240,]  1.5845528807  0.3445231282 -0.272478651  1.454825603 -0.6233202025
## [241,] -1.1153339245  0.9284920103 -1.425772808  0.817089168 -0.3921075456
## [242,]  0.1514350674 -0.0946406719 -0.023153129  0.525905682 -0.4341328443
## [243,]  0.1200518159  2.0631355943 -0.104296840 -0.338243733 -1.3731108572
## [244,]  0.2027959021 -0.0849401635  1.463003500 -1.950875326 -0.9218141608
## [245,] -0.7978352078  1.1938858224 -0.299961432  0.614450844  0.9101726144
## [246,]  0.7396572613 -1.8187328378 -0.722086197 -1.493394128  0.4645379441
## [247,] -0.2925104736  1.7654731385  0.900472570 -1.224373692 -1.9931934779
## [248,]  1.5528942911 -0.3823914320  1.036454458 -0.647625094  0.3524471733
## [249,] -1.3878602134  0.1146013481 -0.164370679  1.656090276 -0.3786438121
## [250,]  0.8920970829 -0.2471013297 -1.020127228 -0.368418686 -0.1360227207
## [251,]  0.5619597323  0.8961292302 -1.334701366  0.379131211  0.2574922605
## [252,] -1.9119232499  0.6272419580 -0.040167086  0.267890918 -0.3638157824
## [253,] -0.6003662352 -0.0860071646  0.036601334 -0.492122827  1.7173048359
## [254,] -0.0075139193 -0.5445206700 -0.012862474  0.166851359 -0.9379488813
## [255,] -0.3317993324  1.3861884739  0.366675439 -0.608606841  0.8330237465
## [256,] -0.1633623299  0.3209166774 -1.432590791 -1.371786484 -0.0640701133
## [257,] -0.2232857151 -0.2414764424 -0.056790620  0.475449978 -0.2479260376
## [258,]  0.6025818559 -0.2811734954 -0.100457057  1.230327282 -0.5999538620
## [259,]  0.4170038534  1.6903016657 -0.874392374  0.326717780  0.5784111216
## [260,]  0.0002427880 -2.7793829806 -1.102881662 -0.225616264 -0.1222536990
## [261,]  0.1823409035 -1.1936153031  0.214544196 -0.186836394 -0.3278446880
## [262,] -1.2715304280 -2.7286452138 -0.103067971  0.538373097  0.3577129850
## [263,]  1.4670339885  0.0560863487  1.649570038  0.463640188 -0.2575170414
## [264,] -1.2367743349  0.6690005850  0.825026937  0.357533884  0.3547903089
## [265,]  1.1603304648  0.2564488286 -0.466493609 -0.784972182 -0.9809742273
## [266,] -0.7338553859 -0.0482649295 -0.773772879  0.957953335  0.2606999512
## [267,]  0.8889099300 -0.7066213845 -0.312820562  0.509747636 -0.7811957618
## [268,] -0.5705395526  0.5542518386 -0.472892785  0.313815624  0.5342072708
## [269,] -0.8512332042 -0.4827810745  1.036359939  0.228757735 -1.1577294509
## [270,] -0.3740756655  0.0417266096  0.932044033 -0.273332092  0.2768452963
## [271,]  0.4032019324  0.2527873889 -1.136724346 -0.363677374 -0.7277646423
## [272,] -0.0441355087  0.0294030664 -0.262150079  0.441155012 -0.3627821102
## [273,]  0.3577792653 -0.4086229346 -0.083707788  1.279164475 -0.4796391971
## [274,] -1.5531806436 -0.3803915162  0.949686923  0.343125451  0.2926302275
## [275,] -0.8756634804  0.4962594512  1.171716745  0.439440455 -0.5907452008
## [276,] -0.0669921990  0.2226560485 -0.428683876 -0.958918591  0.3034629867
## [277,] -0.3019960188  0.7735920022  0.079229910  0.654463086  0.3520907959
## [278,]  0.4308091328  1.8659576704 -1.545778625 -1.887880264 -0.4217303502
## [279,] -0.7519674960  1.2586366080 -1.278552065 -1.119937175 -0.5003505269
## [280,]  0.5227459304 -1.1517873688  0.828307407  1.701901555  0.0377575323
## [281,] -1.2891964728  0.7268513687 -0.413380030  0.633575030 -0.5561705670
## [282,]  0.0072723101  0.1177275082 -0.650013848  0.271424375  0.5749921706
## [283,]  1.3745317270 -1.0682943337  1.842989199 -0.939231198  1.3300725948
## [284,]  0.3001583816 -0.6476922795  1.653718382 -1.711975445  0.7720718709
## [285,]  0.0608953430 -0.0522280140 -0.057624847 -0.829450762  0.2804388426
## [286,] -0.3793650617 -0.7280509615  0.123139185  0.461371200  0.5299479216
## [287,]  0.4851285995  0.5384871928 -0.034959347 -1.162760972 -0.2992416890
## [288,]  0.7206171053 -0.5881867306  0.011350392  0.249568814 -0.3876300550
## [289,]  1.2655471357 -0.6204720310  0.636573907  1.855271946 -0.3714336955
## [290,] -1.6098224177  0.6667855015 -0.514808749  0.565964376 -0.4048883452
## [291,]  0.3830414208  1.0109341013 -1.123266595  0.241569021 -0.6783633899
## [292,] -0.6782178362  1.3000455823  0.767054107  0.198642605 -0.6140196286
## [293,]  1.6844910775 -0.0002079914  0.603823492 -1.555022296 -1.0310973402
## [294,] -1.1399821131  0.5706408517  0.225131480  1.006080236  1.1212419211
## [295,]  1.2939157922 -1.0000212360 -0.805579220 -1.173390048  0.5219335656
## [296,] -1.5209166720  0.1111558629  2.082635517 -1.083053578 -1.2292044177
## [297,]  1.7354934370 -0.5086166346  1.274213378 -0.507815962  0.2828894521
## [298,] -1.7703871607 -1.0686169716  0.945636813  1.981196497 -0.0611704156
## [299,]  0.6019869525 -0.0363752051  0.421560655 -0.836265536 -0.6174102949
## [300,]  0.4477745716  0.6016858070 -1.070264315  0.420841396  0.3475341540
## [301,] -1.7409282983  0.6768220842  0.003313970  0.460084373 -0.4587245723
## [302,]  1.0154864475 -0.0985800207 -0.643518629 -0.004429237  1.5584108132
## [303,]  0.4923718799 -0.3707895537  0.066845323  0.432132091 -1.1977180848
## [304,] -0.8242134745 -0.2005517233  1.866263998 -0.162230166  1.2491918924
## [305,] -0.5806708637 -1.0993056715 -0.071064434 -0.836025698  0.2882833788
## [306,] -0.5943934264  0.1107253930 -0.653395882  0.019173765 -0.1081640853
## [307,]  0.5500102538 -0.6588696646  0.287068731  1.294093947 -0.5254052273
## [308,]  0.4272639574  1.5292324864 -0.687199135  0.451762489  0.5889517563
## [309,]  0.5268382605 -2.2511204799 -1.404420153 -0.130277486 -0.4341384337
##                PC11          PC12         PC13         PC14          PC15
##   [1,]  0.420523565  0.4334820544  0.016896184  0.568431041  0.4383575733
##   [2,]  0.462308125  0.3986804449 -0.218844308  0.061830934 -2.0687208915
##   [3,] -1.315721292 -0.6118901582 -1.234182675  0.374500028  0.7773050725
##   [4,] -0.036031283 -0.2638657935 -0.338447239  0.010300783  0.5421504516
##   [5,] -0.912182701 -0.4352120930 -1.415924824  0.029107293  0.2282780957
##   [6,]  0.006675664  1.2983623838 -0.206751142 -0.234096001 -0.6232337130
##   [7,] -0.681612182 -0.4367979407  0.627895778 -0.126860747  0.5778337358
##   [8,]  1.570297126 -0.3494589711 -0.224076737  0.307935702 -0.1791024816
##   [9,]  0.588029356  1.3889527245  0.379929206  0.698899496  0.2331253689
##  [10,]  0.013843135 -0.3935900740  0.183078896 -0.531951622 -0.0795574606
##  [11,] -0.393455043 -0.8581065623  0.256269265 -0.857916040  0.0129291768
##  [12,]  0.012211427  0.7468853985  0.391100484  0.158685593 -0.2626260427
##  [13,]  0.249502857  0.0929055090 -0.044637030  0.616334219 -0.0808919597
##  [14,]  0.108202924  0.0621200579 -0.074766804 -0.009759719  0.1656639689
##  [15,] -0.894184802  0.6667391909 -0.134044309  0.395128230 -0.5965953711
##  [16,]  0.908454725 -0.2179462237  0.185976081 -0.004498742 -0.4711337983
##  [17,] -0.992433913 -0.7479697500 -0.485089739 -0.584556336 -0.1028938720
##  [18,] -0.796874258 -0.9948424816  0.538850685 -0.867448372  0.4749865902
##  [19,] -0.844001807 -0.4463708756  1.628548810 -0.604924292  0.2536040792
##  [20,]  0.320441162  0.1598941284 -0.096108696  0.385799068 -0.0495534724
##  [21,]  0.467789803 -1.2219438435  0.249408139 -0.731181079  0.4061416274
##  [22,]  0.411759401 -0.2953011717 -1.528031755  0.251766287 -0.3967280920
##  [23,]  0.951863976 -0.0769681900 -0.219517073  0.120893372 -0.3421600285
##  [24,]  0.095539826  0.0651550583  0.029651045 -0.012197733  0.1471579650
##  [25,] -0.734840381 -0.7561054781 -0.278001541 -1.273542765  0.0662511665
##  [26,]  0.494253801  0.0829017276 -0.087042222  0.335995178  0.6686192208
##  [27,]  1.219675724  0.3473208400 -0.118633159  1.409979591  1.0286389588
##  [28,] -1.041488146 -0.2161509584 -0.829347522 -0.448322267 -0.2646588750
##  [29,] -0.837946225  0.2926483701  0.133017998  1.000956763  0.8888048793
##  [30,]  0.404992386  0.1465291483  0.689510060 -0.526647777  0.4152453066
##  [31,] -0.863377283  0.8313440043  0.490013777  1.143399608 -0.8880189012
##  [32,]  1.135636716 -0.4148927197 -1.304990553  0.638676216  0.2022641052
##  [33,]  0.828808911 -0.6314252501 -0.319879928 -0.179981187 -0.9960511402
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## [222,]  0.465861696 -1.1847956071  0.607637361 -0.864458757  0.9942057110
## [223,] -0.424516730  1.4748814174  0.145181171  0.420214420  0.8878891898
## [224,]  1.236438417  1.7300181032  0.383479681 -1.797487236 -0.3845053731
## [225,] -0.426387323 -0.2842011807 -0.688413707  0.984933178  0.0919241125
## [226,] -0.263850500 -0.9207747960  0.901682146 -0.143776831 -1.0068171990
## [227,] -0.162814971  0.5436072760  1.690537431  0.239060114 -0.0051335613
## [228,]  1.026434521  0.1900517074  0.077777001 -0.454886610 -0.6582377293
## [229,] -1.572773111 -0.0312910426 -0.288500239  0.789657126  0.2507442514
## [230,]  0.036653223 -1.0775967170  0.277635073  1.607073041 -1.6704573397
## [231,] -0.760711421  0.5801334609 -0.853926932 -1.158985637 -0.8636755088
## [232,]  0.224797306 -0.8638491677  0.369310689 -0.806783880  1.2564088524
## [233,] -0.256109481  0.0813377143  0.160075683 -0.944625884 -0.4426724802
## [234,] -0.500478173  1.1402854283  0.940682998  1.603648258 -0.5339839208
## [235,]  0.420557609  1.1757651232  1.405814095 -0.660944846 -0.4584058641
## [236,]  1.601474335  0.0329770609 -0.786863332  0.850110349  0.5049464856
## [237,] -0.245442814  0.5299043586  0.123567074 -0.198453838  0.2846141257
## [238,] -1.677910380  0.9370002172  0.587961195 -0.028877664 -0.3326711026
## [239,] -0.615963168  0.4614410046 -1.373119458 -0.462593734  0.5385699125
## [240,]  0.346190183 -0.1741353115 -1.640682285  0.219620922 -0.4347494070
## [241,] -0.237700953 -1.8269571358 -1.733722502 -0.868267167  0.0739759153
## [242,]  0.189743967 -0.4365589058 -0.484810381 -0.440615878  0.5517758465
## [243,] -0.157734030  1.3944431466 -1.315420940 -1.163315747 -1.0278137201
## [244,]  1.482778302 -1.2292871843  0.735433828 -0.310230712  0.2165680484
## [245,]  0.458353115  1.2794759823 -1.481894590  0.305867734  1.0478414078
## [246,] -0.561798075  1.1599444136 -0.106549811  0.174440364 -0.5614477491
## [247,] -0.904030686  0.1899898851  0.077693633  0.746239059  0.9884091324
## [248,]  0.367306846  0.0797105468  0.421658844 -0.727251810  0.5237866907
## [249,] -0.771447964  0.3220145131  0.421694621 -1.015059403 -0.5611796464
## [250,]  0.891226655  1.8559091541  1.012247198  0.055194895 -0.9096856467
## [251,]  1.865768690 -0.2969116509 -0.060634134 -0.875628676 -0.9524645024
## [252,] -0.460426027 -0.7028922394 -1.480131889 -0.915330523  0.4818986921
## [253,]  0.383069666  0.0729546428  0.084302734  0.102023258 -0.1799652501
## [254,] -0.073701024 -0.5385788237 -0.284734897 -0.129813506  0.0242731252
## [255,] -0.316718368  1.3263872034  0.646147689 -0.380331569 -0.1411549227
## [256,] -0.020055754 -1.7066672359  1.308291456  1.314337165 -0.4218148172
## [257,]  0.099230582  0.0633414172 -0.089809685 -0.030062396  0.1705910065
## [258,] -0.814719325  0.3554712920 -0.482169057  0.167179178 -0.3464488494
## [259,]  0.827465657 -0.2784515308  0.408041681  0.443426503  0.6190726633
## [260,]  1.969911006  0.1981480175 -0.131559676 -0.025757074 -0.6685676214
## [261,]  0.120692741  1.5520772439  1.851214993 -0.252163607  1.6108503758
## [262,]  0.382435126 -0.0915046435  0.031776181 -0.399960814  0.6689254912
## [263,] -1.094660807  0.5313274642 -0.723942851  0.793217363 -0.4923627949
## [264,]  0.077558875  1.0730493255 -0.864140025 -0.451585611 -0.3669914933
## [265,] -0.792476333 -0.1982225738  0.358157169 -0.161823863  0.5066678723
## [266,]  1.553818534 -0.4152766906 -0.754771835  0.100342799 -0.0263940820
## [267,]  0.786240415  0.5920760463 -0.296554785  0.146965215  0.8331283743
## [268,] -0.077097448 -0.1064969348  0.735943782 -0.312441464 -0.3501374412
## [269,] -0.507108198 -0.1399924983  1.449425933 -0.110453136 -0.6621996038
## [270,]  0.040436218  0.8904793243  1.394424602  0.565017503 -0.5631495248
## [271,]  0.271097474 -0.1892803429 -0.938504400  0.190741482  0.2747592430
## [272,]  0.074050682  0.1269508821 -0.024944975 -0.003253330  0.1234850640
## [273,] -0.931853006  1.0078033725  0.209204840  0.739747383 -0.8785993809
## [274,]  0.836197278  0.0005452163 -0.200324353 -0.003385652 -0.5181722760
## [275,] -0.841050307 -1.1692393307 -0.517406569 -0.715403414  0.1361235206
## [276,] -0.983023515 -0.1041939949  1.271501292 -0.181852971 -0.2020560780
## [277,] -0.801581787 -0.5012883274  1.399310331 -0.619467237  0.3217333923
## [278,]  0.235167642  0.0761654172 -0.868124389 -0.030755816  0.1837052038
## [279,]  0.259645931 -0.7659212831 -0.171331327 -0.771443767  0.2503776820
## [280,]  0.386626612  0.0020122656 -1.394599751  0.535355543 -0.6125133511
## [281,]  0.802480244 -0.1790725087 -0.588888791 -0.368026445 -0.1555218514
## [282,]  0.482401592  0.8485498995 -0.439878351  0.187371367 -0.9810781952
## [283,]  0.133037414  0.6534827324 -1.212225499  0.499259150 -0.6413672907
## [284,]  0.406502194  0.7165172399  0.480778116  0.925558289  0.1639291407
## [285,] -0.857974639 -0.6741941727  0.840754566 -0.600815722  0.2219338890
## [286,]  0.038978935 -0.7220043659  0.586611893  0.752720450 -0.5492553667
## [287,]  0.400500823 -0.3586637134 -0.511835579 -0.069931664  0.3513372646
## [288,]  0.822793804 -1.1842067114 -0.215174410 -0.208041555  0.5787408975
## [289,]  0.367378840  0.0070424388 -1.070586440  0.564778180 -0.6732674459
## [290,]  0.707731574  0.3200376804 -0.202871587  0.031149299 -0.5331046573
## [291,] -0.081437579  0.6813613159  0.423020726  0.339802365 -0.2840377311
## [292,] -0.448238235  0.5883060329  0.080163844 -0.336205536 -0.5854681151
## [293,]  1.782082642 -0.8786251058  0.424369024  0.453352217  0.1686013563
## [294,]  0.262999653  2.5161366718  0.184353081  1.516995025 -0.0388854969
## [295,] -1.028991209 -0.2410878726 -0.813808730 -0.445286831 -0.2550268203
## [296,] -0.767768447 -0.1184498761 -0.336592138  0.625874697  1.2319341578
## [297,]  0.424298678 -0.1658003787  0.354749610 -0.877756151  0.6822191559
## [298,] -0.583145614 -0.3361529386  0.012495691 -1.390367906 -0.1025393108
## [299,] -0.021967799 -0.5455360842 -0.094936125 -0.461983720  1.6215068235
## [300,]  1.938133198 -0.6013023488 -0.357609883 -1.101025575 -0.7146842916
## [301,] -0.568533563 -0.1138279703 -0.613242911 -0.355154778 -0.0453825308
## [302,]  0.737361526  0.1736037657 -0.361233504  0.692900730 -0.0526630204
## [303,] -0.126718864 -0.2544281997  0.408186660  0.192943852 -0.2835720653
## [304,] -0.061479981  0.4313114021  0.099934079 -0.890448988  0.4808252877
## [305,]  0.093734175 -1.8826517649  1.632717238  1.431294242 -0.4038404559
## [306,]  0.087368328 -0.0350587299 -0.772962725 -0.292136488  0.3733408245
## [307,] -0.674268055 -0.2830235204 -1.093907597 -0.326910311  0.1536629841
## [308,]  0.814679485 -0.1524666351  0.681117266  0.601996141  0.4859256479
## [309,]  1.875453301  0.5883067607  0.490080068  0.307284192 -1.0199760971
##                PC16         PC17
##   [1,] -0.204699168  0.399778790
##   [2,]  0.045288943  0.292915024
##   [3,] -0.271595154 -0.814045516
##   [4,] -0.371673537  1.078203419
##   [5,]  0.734034423  0.516096799
##   [6,]  0.370839736  0.464690533
##   [7,] -0.322143489  0.050306784
##   [8,]  0.531051672  0.194644777
##   [9,] -1.124665269 -0.473960208
##  [10,]  0.076492553  0.033336741
##  [11,] -0.534141622 -0.128982341
##  [12,]  0.084037407 -0.456830857
##  [13,]  0.189629446  0.456895464
##  [14,] -0.016716439 -0.021511422
##  [15,]  0.006422442 -0.329564249
##  [16,] -0.225723824 -0.788232416
##  [17,]  0.487690414 -0.355745563
##  [18,] -0.216253994  0.281111017
##  [19,] -0.357368372 -0.574817902
##  [20,] -0.121585264  0.153361961
##  [21,] -0.325279346  0.341539699
##  [22,] -0.249217026 -0.517074387
##  [23,] -0.474336582  0.001382573
##  [24,]  0.020601136 -0.029383874
##  [25,] -0.421748563 -0.176386698
##  [26,] -0.375057468  0.459319241
##  [27,]  0.157050749  1.283191589
##  [28,]  0.172160415 -1.177121386
##  [29,]  0.840632915  0.308201578
##  [30,]  0.546906491  0.990041317
##  [31,]  1.833637726  0.602301402
##  [32,]  0.899009190 -0.685671003
##  [33,]  0.778795299  0.192681525
##  [34,]  0.282663097  0.192190653
##  [35,] -0.281726780 -0.102251797
##  [36,]  0.404702630  0.315448071
##  [37,]  0.252701007 -0.080408534
##  [38,]  0.835870432 -0.173405499
##  [39,]  0.794453324 -0.901139864
##  [40,] -0.664108490 -0.302257112
##  [41,] -0.699334673 -0.772619337
##  [42,]  0.302214498  0.526431365
##  [43,]  0.215644055  0.008363015
##  [44,]  1.218170500 -0.374050417
##  [45,] -0.107189826  1.558186080
##  [46,] -0.014697978 -0.110994738
##  [47,] -0.314501834  1.085094010
##  [48,] -0.453323188  1.568209576
##  [49,]  0.371135730 -0.880906339
##  [50,]  0.038378647 -1.504845090
##  [51,] -0.190277899 -0.215343711
##  [52,]  0.571180847 -0.485102183
##  [53,] -0.795216391  0.307609636
##  [54,]  0.101171607 -0.457206584
##  [55,] -0.836682394  1.227393045
##  [56,] -0.761838666  0.044936466
##  [57,] -0.093377912  0.519556971
##  [58,] -0.085545972  0.334201010
##  [59,]  0.820792154  0.214839663
##  [60,]  0.108966172 -0.162975362
##  [61,] -0.542958636  1.037635542
##  [62,] -1.090814185 -0.173869707
##  [63,]  0.397950756  0.601928262
##  [64,] -0.286457614 -0.316048608
##  [65,]  1.423427877  0.100505316
##  [66,] -1.311470262 -0.340525215
##  [67,] -0.360979053  0.384060109
##  [68,]  0.046545960  0.364930671
##  [69,]  0.851869088  0.039331283
##  [70,]  0.125575693  0.027204718
##  [71,]  0.339668208  0.511883358
##  [72,]  0.135095885 -0.227962988
##  [73,] -0.161028009 -0.359990351
##  [74,] -0.151488592  0.364242693
##  [75,]  0.032547772 -0.019961277
##  [76,] -0.125258951 -0.040086038
##  [77,] -0.314385878 -0.543428311
##  [78,] -0.335717440  0.228175597
##  [79,]  0.400994735 -0.072763914
##  [80,] -0.528254127  0.151448992
##  [81,]  0.139513375  0.283297565
##  [82,] -0.005952746  0.259756203
##  [83,]  0.220449326  0.205910512
##  [84,]  0.821389639 -0.280463409
##  [85,] -0.616768168 -0.143967535
##  [86,]  0.587250538  0.095098054
##  [87,] -0.057818756 -0.333248457
##  [88,] -0.618241629  0.030801222
##  [89,]  0.262114853  0.284029297
##  [90,] -0.441595058  0.570186068
##  [91,]  0.546853402  0.247395413
##  [92,] -0.954452414 -0.237225566
##  [93,] -0.690367526  0.648356547
##  [94,]  1.196418062 -0.755162981
##  [95,] -1.025634831  0.626103061
##  [96,] -0.491732734 -0.231372581
##  [97,]  0.162249355  0.180426095
##  [98,]  0.601243917 -0.104024116
##  [99,] -1.217306954 -0.042251874
## [100,]  0.210795257 -0.266528766
## [101,]  0.009178791 -0.140306083
## [102,] -0.239832184 -0.505299089
## [103,] -0.001081145  0.061331010
## [104,]  0.225753874  0.024185581
## [105,] -0.423907862  0.044826848
## [106,] -0.049813183  0.066391359
## [107,]  0.144666199  0.249381777
## [108,]  0.288291683  0.147150980
## [109,]  0.683932546 -0.766405649
## [110,] -0.165238363  0.413606088
## [111,] -0.311500803  0.275308649
## [112,]  0.470357058  0.841243335
## [113,]  0.222169322 -1.078565979
## [114,] -0.168079224  0.872922772
## [115,]  0.877633521  1.155793976
## [116,]  0.248481964  0.515447773
## [117,] -0.215599949  0.058770936
## [118,]  0.514993586  0.210590031
## [119,] -0.226150793 -0.086942561
## [120,]  0.289380434  0.313280968
## [121,]  0.215127207 -0.235851294
## [122,]  0.018379895 -0.540713487
## [123,] -0.445011923 -1.187395940
## [124,] -0.197477228  0.266806473
## [125,] -0.289242777 -0.037798448
## [126,] -0.565139828 -0.738008042
## [127,] -0.159623044 -0.074763111
## [128,]  0.075685920  0.058279950
## [129,] -0.639909303  0.323712286
## [130,]  0.029766279  0.032157735
## [131,]  0.251431807  0.393080370
## [132,]  0.099890861 -0.888438144
## [133,]  0.278208194  0.028194637
## [134,] -0.035768643  0.342225755
## [135,] -0.465900314 -0.053961025
## [136,] -0.579918745 -0.349760333
## [137,]  0.000772863  0.151658109
## [138,]  0.209223668 -1.243826974
## [139,]  0.869070173  0.233877079
## [140,]  0.805399365  0.872283165
## [141,]  0.341425105  0.022592252
## [142,] -0.684397168 -0.936264140
## [143,]  0.869141848 -0.006288726
## [144,] -0.404210072 -0.522821842
## [145,]  0.676296036 -0.021386986
## [146,]  0.152334617 -0.236617040
## [147,]  0.100548266  0.546407053
## [148,] -0.614292886  0.646342147
## [149,]  0.157997524  0.030636773
## [150,] -0.396764299 -0.190573406
## [151,] -0.644069677 -0.846298375
## [152,]  0.284353292  0.503158969
## [153,]  0.173424869  0.019842343
## [154,]  0.044405912 -0.388242074
## [155,]  0.824834606  0.325438074
## [156,]  0.121962865 -0.861216712
## [157,] -0.442513188  0.702610115
## [158,]  0.793495320  0.334082201
## [159,]  0.447669504 -1.216843843
## [160,]  0.090886418 -1.371108370
## [161,] -0.438017503  0.002962693
## [162,]  0.541409695 -0.450589729
## [163,] -0.820401346  0.677621810
## [164,]  0.226252313 -0.216161914
## [165,] -0.677481397  1.415588471
## [166,] -0.583691233  0.119191040
## [167,]  0.293109180  0.174793193
## [168,] -0.203669862  0.239594626
## [169,]  0.743351273  0.219123542
## [170,]  0.130802257 -0.400058587
## [171,] -0.410579567  0.611738612
## [172,] -1.026212619 -0.272878294
## [173,]  0.242101208  0.488238862
## [174,] -0.288948646 -0.279987488
## [175,]  1.601354083 -0.114113845
## [176,] -1.520591312 -0.365248874
## [177,] -0.085103098  0.421068268
## [178,]  0.047903515  0.346408715
## [179,]  0.290577969  0.257721538
## [180,]  0.058594121 -0.016260362
## [181,]  0.351179366  0.395519794
## [182,]  0.067019098  0.018984832
## [183,]  0.069867765 -0.454941763
## [184,]  0.068081891  0.334040887
## [185,] -0.180412417  0.376233283
## [186,] -0.039127144  0.230944364
## [187,] -0.461598407 -0.299418857
## [188,] -0.863571623  0.415674312
## [189,]  0.164826381 -0.745791996
## [190,]  0.055938829 -0.226902271
## [191,] -1.130935409  0.447494847
## [192,] -0.780931794 -0.127862513
## [193,] -0.218573295 -0.492468351
## [194,] -0.164408869 -0.368908455
## [195,] -0.723395579  0.067538846
## [196,]  0.685196206  0.204171257
## [197,]  0.169355098 -0.549958598
## [198,] -0.769993878  0.122808536
## [199,]  0.128325234  0.614367708
## [200,] -0.115885447  0.264880595
## [201,]  0.569809145  0.268030342
## [202,] -1.012129894 -0.350160623
## [203,] -0.449618464  0.852052206
## [204,]  1.060227957 -0.534824136
## [205,] -0.614394865  0.846168128
## [206,] -0.773683331  0.063697140
## [207,]  0.510641502  0.044842721
## [208,]  0.539028601 -0.851370448
## [209,] -1.093386790 -0.122726928
## [210,] -0.155246654  0.001096426
## [211,] -0.194613598 -0.072297240
## [212,] -0.321072705 -0.504598778
## [213,]  0.179998006 -0.184224234
## [214,]  0.259444768  0.009943970
## [215,] -0.780618138  0.139516314
## [216,] -0.198320989  0.234820841
## [217,]  0.268641865  0.234126153
## [218,]  0.453731649 -0.077289733
## [219,]  1.088579218 -0.729502626
## [220,] -0.676442863  0.168806418
## [221,]  0.347355852 -1.056801166
## [222,] -0.165990170 -1.283069689
## [223,]  0.332638512 -0.293672149
## [224,]  0.795452124 -0.679781217
## [225,] -0.988260241  0.662611902
## [226,]  0.110787399 -0.291810588
## [227,] -0.252893278  0.923464117
## [228,] -0.433616613  0.144755671
## [229,]  0.066773967  0.275017663
## [230,]  0.063241523 -0.101200129
## [231,]  1.179012497  0.462607684
## [232,] -0.019352945 -0.148293626
## [233,] -0.615282088  0.926318797
## [234,] -0.681058673 -0.744278153
## [235,]  0.786713435  0.356755296
## [236,] -0.374744887 -0.315348333
## [237,]  1.269945960  0.064941224
## [238,] -1.574325649 -0.425168932
## [239,] -0.740202720  0.388446323
## [240,] -0.117226699 -0.428558305
## [241,]  0.955826543 -0.268608022
## [242,] -0.232986784  0.174246513
## [243,] -0.030911579 -0.178010067
## [244,] -1.116037385 -0.443587411
## [245,]  0.040368748  0.267750892
## [246,]  1.404264474 -1.478292614
## [247,]  0.978839680  0.483021714
## [248,]  0.603511293  1.157426119
## [249,]  0.692486224  0.040663628
## [250,] -0.722358199 -0.980492359
## [251,]  0.905558470  0.015177064
## [252,] -0.818092266 -0.133033980
## [253,]  0.321527445 -0.257408901
## [254,] -0.070998352  0.016638914
## [255,]  0.637360258  0.497985009
## [256,] -0.183950774  0.629102932
## [257,]  0.001359994 -0.002573657
## [258,] -0.199281757 -0.231513525
## [259,] -0.767591488 -0.674397629
## [260,]  0.473512663  0.278870895
## [261,]  0.279643315 -0.373044027
## [262,]  1.231233143 -0.616917441
## [263,]  1.196629303  0.206480172
## [264,]  0.154833871  0.622433628
## [265,] -0.106378218  0.206223917
## [266,]  0.516903811  0.396282048
## [267,] -1.619758037 -0.272082445
## [268,]  0.326323508 -0.089511243
## [269,] -0.174273385 -0.580481396
## [270,]  0.117172450 -0.841650045
## [271,]  0.058390380  0.788983893
## [272,]  0.062226434 -0.005549539
## [273,]  0.120922819 -0.511551264
## [274,] -0.104788706 -0.658045736
## [275,]  0.155305470 -0.417142635
## [276,]  0.258037515  0.001018338
## [277,] -0.471111047 -0.560894424
## [278,] -0.009003091  0.546602298
## [279,]  0.087872999  0.607421705
## [280,] -0.181710770 -0.644080424
## [281,] -0.184704565  0.404085944
## [282,]  0.381975583 -0.300021491
## [283,] -0.599984450 -0.026298504
## [284,] -0.130302106  0.170677295
## [285,] -0.054769022  0.159784347
## [286,] -0.357835410  0.115076387
## [287,] -0.335197519  0.362168104
## [288,]  0.068117172  0.532982330
## [289,] -0.109459288 -0.700975579
## [290,]  0.057996353  0.237331002
## [291,]  0.442745185 -0.109642684
## [292,] -0.638324403  0.131842402
## [293,] -0.586836031 -0.339105240
## [294,]  0.622801658 -0.405256743
## [295,]  0.146444590 -1.191554915
## [296,]  0.643560584  0.500112321
## [297,]  0.473122824  1.188323428
## [298,]  0.244203227  0.124670211
## [299,] -0.932773979 -0.723538859
## [300,]  0.720091571  0.108483530
## [301,] -0.501085666 -0.447556210
## [302,]  0.718340959 -0.098268391
## [303,]  0.109617474 -0.207952469
## [304,]  0.030515055  0.610897882
## [305,] -0.400852865  0.425130764
## [306,] -0.037178820  0.247090067
## [307,] -0.562633443 -0.019336438
## [308,] -0.714004235 -0.783153726
## [309,]  0.737576367  0.096973111
plot(cancer_pca)

#get the original value of the data based on PCA
center <- cancer_pca$center
scale <- cancer_pca$scale
new_cancer <- as.matrix(cancer[,-1])
new_cancer
##        GENDER AGE SMOKING YELLOW_FINGERS ANXIETY PEER_PRESSURE CHRONIC_DISEASE
##   [1,]      0  69       1              1       1             0               0
##   [2,]      0  74       0              0       0             0               1
##   [3,]      1  59       1              0       0             1               0
##   [4,]      0  63       0              1       1             0               0
##   [5,]      1  63       1              1       0             0               0
##   [6,]      1  75       1              1       0             0               1
##   [7,]      0  52       0              0       0             0               0
##   [8,]      1  51       0              1       1             1               0
##   [9,]      1  68       0              0       1             0               0
##  [10,]      0  53       0              1       1             1               1
##  [11,]      1  61       0              1       1             1               1
##  [12,]      0  72       1              0       0             0               1
##  [13,]      1  60       0              0       0             0               0
##  [14,]      0  58       0              0       0             0               0
##  [15,]      0  69       0              0       0             0               0
##  [16,]      1  48       1              1       1             1               1
##  [17,]      0  75       0              0       0             0               1
##  [18,]      0  57       0              1       1             1               1
##  [19,]      1  68       0              1       1             1               1
##  [20,]      1  61       1              0       0             0               1
##  [21,]      1  44       0              1       1             1               1
##  [22,]      1  64       1              1       1             1               0
##  [23,]      1  21       0              0       0             0               1
##  [24,]      0  60       0              0       0             0               0
##  [25,]      0  72       0              1       1             1               1
##  [26,]      0  65       1              1       1             0               0
##  [27,]      1  61       0              1       1             0               0
##  [28,]      0  69       1              0       0             1               0
##  [29,]      1  53       0              1       1             0               1
##  [30,]      0  55       1              1       0             0               0
##  [31,]      1  57       0              1       0             0               0
##  [32,]      0  62       0              0       1             0               0
##  [33,]      0  56       0              1       1             0               0
##  [34,]      1  67       0              1       1             0               1
##  [35,]      0  59       1              1       1             0               0
##  [36,]      1  59       0              1       1             0               1
##  [37,]      0  60       1              1       0             0               1
##  [38,]      1  56       1              0       0             0               1
##  [39,]      0  56       0              0       0             0               1
##  [40,]      0  60       0              0       0             0               1
##  [41,]      0  68       0              0       1             0               0
##  [42,]      0  63       1              0       0             1               0
##  [43,]      1  77       1              1       1             1               1
##  [44,]      0  52       0              0       0             1               0
##  [45,]      1  70       0              1       0             1               1
##  [46,]      0  72       0              1       1             1               1
##  [47,]      0  62       0              1       0             0               1
##  [48,]      1  64       0              1       0             1               0
##  [49,]      1  70       1              0       1             1               1
##  [50,]      0  60       1              0       1             1               1
##  [51,]      1  56       1              0       0             1               1
##  [52,]      0  63       0              1       1             0               1
##  [53,]      1  54       0              0       0             1               0
##  [54,]      0  49       0              0       0             1               1
##  [55,]      1  57       1              1       0             1               1
##  [56,]      0  52       1              1       1             0               1
##  [57,]      1  63       1              1       0             1               0
##  [58,]      0  73       1              0       0             0               1
##  [59,]      0  47       1              1       0             1               1
##  [60,]      0  69       0              1       1             1               0
##  [61,]      0  70       1              1       0             1               1
##  [62,]      1  60       1              1       1             0               0
##  [63,]      0  70       1              1       0             1               0
##  [64,]      1  68       1              0       1             0               1
##  [65,]      0  74       1              1       0             1               0
##  [66,]      1  71       0              1       1             1               1
##  [67,]      1  56       1              1       0             0               1
##  [68,]      0  66       0              0       0             0               0
##  [69,]      1  76       0              1       1             1               0
##  [70,]      1  78       0              1       1             1               0
##  [71,]      0  68       0              1       1             1               0
##  [72,]      1  66       0              1       1             1               0
##  [73,]      0  67       1              0       0             0               1
##  [74,]      1  60       0              0       0             0               1
##  [75,]      0  61       0              0       0             0               0
##  [76,]      0  58       0              0       0             0               0
##  [77,]      1  76       1              1       1             1               1
##  [78,]      0  56       0              0       0             0               0
##  [79,]      0  67       0              1       1             1               1
##  [80,]      1  73       0              1       1             1               0
##  [81,]      1  58       1              0       0             0               0
##  [82,]      1  54       0              1       1             1               1
##  [83,]      1  62       0              1       1             1               1
##  [84,]      1  81       1              0       0             1               1
##  [85,]      0  56       1              0       0             0               1
##  [86,]      0  60       1              1       1             0               0
##  [87,]      0  66       1              1       1             0               1
##  [88,]      0  62       1              1       1             0               0
##  [89,]      1  62       0              1       1             0               1
##  [90,]      1  55       0              0       0             1               1
##  [91,]      1  62       1              0       0             1               0
##  [92,]      1  71       1              0       0             0               1
##  [93,]      0  52       0              0       0             0               1
##  [94,]      1  59       1              1       1             1               1
##  [95,]      0  48       0              0       0             0               1
##  [96,]      0  60       1              1       1             1               0
##  [97,]      1  61       0              1       1             0               0
##  [98,]      0  59       0              0       0             1               0
##  [99,]      0  64       1              1       1             1               0
## [100,]      0  56       0              0       0             0               0
## [101,]      0  58       0              0       0             0               0
## [102,]      1  81       1              1       1             1               1
## [103,]      0  64       0              0       0             0               0
## [104,]      0  62       0              1       1             1               1
## [105,]      1  72       0              1       1             1               0
## [106,]      1  60       1              0       0             0               1
## [107,]      1  61       0              1       1             1               1
## [108,]      1  60       0              1       1             1               1
## [109,]      1  49       1              0       0             1               1
## [110,]      0  53       1              0       0             0               1
## [111,]      0  58       1              1       1             0               0
## [112,]      0  61       0              1       1             0               0
## [113,]      1  68       1              0       0             1               0
## [114,]      0  60       0              1       1             0               0
## [115,]      1  72       1              1       0             0               0
## [116,]      1  72       1              1       0             0               1
## [117,]      0  57       0              0       0             0               0
## [118,]      1  51       0              1       1             1               0
## [119,]      1  54       0              1       1             1               0
## [120,]      1  56       1              1       1             1               0
## [121,]      0  77       0              1       1             1               0
## [122,]      0  64       1              0       0             0               1
## [123,]      0  57       0              0       1             0               1
## [124,]      1  66       0              1       1             0               1
## [125,]      0  70       0              0       0             0               0
## [126,]      1  53       1              1       1             1               1
## [127,]      0  51       0              0       0             0               0
## [128,]      0  58       0              1       1             1               1
## [129,]      1  58       0              1       1             1               0
## [130,]      1  63       1              0       0             0               1
## [131,]      1  51       0              1       1             1               0
## [132,]      1  61       1              1       1             1               0
## [133,]      1  61       0              0       0             0               1
## [134,]      0  76       0              0       0             0               0
## [135,]      0  71       0              1       1             0               1
## [136,]      0  69       1              0       1             0               0
## [137,]      1  56       0              1       1             0               0
## [138,]      0  67       1              0       0             1               0
## [139,]      1  54       0              1       1             0               1
## [140,]      0  63       1              1       0             0               0
## [141,]      1  47       0              1       0             1               1
## [142,]      0  62       0              0       1             0               0
## [143,]      0  65       0              1       1             1               0
## [144,]      1  63       0              1       1             1               1
## [145,]      0  64       1              1       1             1               0
## [146,]      1  65       0              1       1             1               0
## [147,]      0  51       1              1       0             0               1
## [148,]      1  56       1              0       0             1               1
## [149,]      0  70       0              0       0             0               0
## [150,]      0  58       0              0       0             0               0
## [151,]      0  67       0              0       1             0               0
## [152,]      0  62       1              0       0             1               0
## [153,]      1  74       1              1       1             1               1
## [154,]      0  69       0              0       0             1               0
## [155,]      1  64       0              1       0             1               1
## [156,]      0  75       0              1       1             1               1
## [157,]      0  47       0              1       0             0               1
## [158,]      1  57       0              1       0             1               0
## [159,]      1  56       1              0       1             1               1
## [160,]      0  68       1              0       1             1               1
## [161,]      1  55       1              0       0             1               1
## [162,]      0  62       0              1       1             0               1
## [163,]      1  73       0              0       0             1               0
## [164,]      0  68       0              0       0             1               1
## [165,]      1  75       1              1       0             1               1
## [166,]      0  63       1              1       1             0               1
## [167,]      1  61       1              1       0             1               0
## [168,]      0  62       1              0       0             0               1
## [169,]      0  44       1              1       0             1               1
## [170,]      0  56       0              1       1             1               0
## [171,]      0  54       1              1       0             1               1
## [172,]      1  57       1              1       1             0               0
## [173,]      0  56       1              1       0             1               0
## [174,]      1  69       1              0       1             0               1
## [175,]      0  72       1              1       0             1               0
## [176,]      1  59       0              1       1             1               1
## [177,]      1  70       1              1       0             0               1
## [178,]      0  64       0              0       0             0               0
## [179,]      1  61       0              1       1             1               0
## [180,]      1  72       0              1       1             1               0
## [181,]      0  63       0              1       1             1               0
## [182,]      1  74       0              1       1             1               0
## [183,]      0  71       1              0       0             0               1
## [184,]      1  71       0              0       0             0               1
## [185,]      0  72       0              0       0             0               0
## [186,]      0  77       0              0       0             0               0
## [187,]      1  72       1              1       1             1               1
## [188,]      0  55       0              0       0             0               0
## [189,]      0  65       0              1       1             1               1
## [190,]      1  67       0              1       1             1               0
## [191,]      1  69       1              0       0             0               1
## [192,]      1  55       0              1       1             1               1
## [193,]      1  51       0              1       1             1               1
## [194,]      1  64       1              0       0             1               1
## [195,]      0  63       1              0       0             0               1
## [196,]      0  69       1              1       1             0               0
## [197,]      0  64       1              1       1             0               1
## [198,]      0  59       1              1       1             0               0
## [199,]      1  73       0              1       1             0               1
## [200,]      1  55       0              0       0             1               1
## [201,]      1  63       1              0       0             1               0
## [202,]      1  60       1              0       0             0               1
## [203,]      0  74       0              0       0             0               1
## [204,]      1  65       1              1       1             1               1
## [205,]      0  79       0              0       0             0               1
## [206,]      0  62       1              1       1             1               0
## [207,]      1  71       0              1       1             0               0
## [208,]      0  63       0              0       0             1               0
## [209,]      0  67       1              1       1             1               0
## [210,]      0  55       0              0       0             0               0
## [211,]      0  54       0              0       0             0               0
## [212,]      1  77       1              1       1             1               1
## [213,]      0  58       0              0       0             0               0
## [214,]      0  64       0              1       1             1               1
## [215,]      1  61       0              1       1             1               0
## [216,]      1  62       1              0       0             0               1
## [217,]      1  67       0              1       1             1               1
## [218,]      1  56       0              1       1             1               1
## [219,]      1  70       1              0       0             1               1
## [220,]      0  70       1              0       0             0               1
## [221,]      1  57       1              0       1             1               1
## [222,]      0  61       1              0       1             1               1
## [223,]      1  77       1              0       0             1               1
## [224,]      0  63       0              1       1             0               1
## [225,]      1  62       0              0       0             1               0
## [226,]      0  59       0              0       0             1               1
## [227,]      1  70       1              1       0             1               1
## [228,]      0  71       1              1       1             0               1
## [229,]      1  56       1              1       0             1               0
## [230,]      0  57       1              0       0             0               1
## [231,]      0  78       1              1       0             1               1
## [232,]      0  64       0              1       1             1               0
## [233,]      0  62       1              1       0             1               1
## [234,]      1  49       1              1       1             0               0
## [235,]      0  77       1              1       0             1               0
## [236,]      1  64       1              0       1             0               1
## [237,]      0  63       1              1       0             1               0
## [238,]      1  54       0              1       1             1               1
## [239,]      1  38       1              1       0             0               1
## [240,]      1  75       1              1       1             1               0
## [241,]      1  70       0              0       0             1               1
## [242,]      0  59       0              0       0             0               0
## [243,]      0  77       0              1       1             0               1
## [244,]      0  61       1              0       1             0               1
## [245,]      1  64       0              1       1             0               0
## [246,]      0  59       1              0       0             1               0
## [247,]      1  71       0              1       1             0               1
## [248,]      0  67       1              1       0             0               0
## [249,]      1  64       0              1       0             1               1
## [250,]      0  68       0              0       1             0               0
## [251,]      0  69       0              1       1             1               0
## [252,]      1  64       0              1       1             1               1
## [253,]      0  59       1              1       1             1               1
## [254,]      1  67       0              1       1             1               0
## [255,]      0  74       1              1       0             0               1
## [256,]      1  77       1              0       0             1               1
## [257,]      0  60       0              0       0             0               0
## [258,]      0  64       0              0       0             0               0
## [259,]      0  70       0              0       1             0               0
## [260,]      0  58       1              0       0             1               0
## [261,]      1  59       1              1       1             1               1
## [262,]      0  39       0              0       0             1               0
## [263,]      1  67       1              1       0             0               0
## [264,]      1  71       1              1       0             0               1
## [265,]      0  70       0              0       0             0               0
## [266,]      1  60       0              1       1             1               0
## [267,]      1  55       0              0       1             0               0
## [268,]      0  60       0              1       1             1               1
## [269,]      1  55       0              1       1             1               1
## [270,]      0  55       1              0       0             0               1
## [271,]      1  70       0              0       0             0               0
## [272,]      0  63       0              0       0             0               0
## [273,]      0  64       0              0       0             0               0
## [274,]      1  59       1              1       1             1               1
## [275,]      0  56       0              0       0             0               1
## [276,]      0  64       0              1       1             1               1
## [277,]      1  62       0              1       1             1               1
## [278,]      1  87       1              0       0             0               1
## [279,]      1  77       0              1       1             1               1
## [280,]      1  59       1              1       1             1               0
## [281,]      1  59       0              0       0             0               1
## [282,]      0  55       0              0       0             0               0
## [283,]      0  46       1              1       1             0               0
## [284,]      0  60       1              1       1             0               0
## [285,]      0  58       0              1       1             1               1
## [286,]      1  58       0              1       1             1               0
## [287,]      1  63       1              0       0             0               1
## [288,]      1  51       0              1       1             1               0
## [289,]      1  61       1              1       1             1               0
## [290,]      1  61       0              0       0             0               1
## [291,]      0  76       0              0       0             0               0
## [292,]      0  71       0              1       1             0               1
## [293,]      0  69       1              0       1             0               0
## [294,]      1  56       0              1       1             0               0
## [295,]      0  67       1              0       0             1               0
## [296,]      1  54       0              1       1             0               1
## [297,]      0  63       1              1       0             0               0
## [298,]      1  47       0              1       0             1               1
## [299,]      0  62       0              0       1             0               0
## [300,]      0  65       0              1       1             1               0
## [301,]      1  63       0              1       1             1               1
## [302,]      0  64       1              1       1             1               0
## [303,]      1  65       0              1       1             1               0
## [304,]      0  51       1              1       0             0               1
## [305,]      1  56       1              0       0             1               1
## [306,]      0  70       0              0       0             0               0
## [307,]      0  58       0              0       0             0               0
## [308,]      0  67       0              0       1             0               0
## [309,]      0  62       1              0       0             1               0
##        FATIGUE ALLERGY WHEEZING ALCOHOL_CONSUMING COUGHING SHORTNESS_OF_BREATH
##   [1,]       1       0        1                 1        1                   1
##   [2,]       1       1        0                 0        0                   1
##   [3,]       1       0        1                 0        1                   1
##   [4,]       0       0        0                 1        0                   0
##   [5,]       0       0        1                 0        1                   1
##   [6,]       1       1        1                 0        1                   1
##   [7,]       1       0        1                 1        1                   1
##   [8,]       1       1        0                 0        0                   1
##   [9,]       1       0        0                 0        0                   0
##  [10,]       0       1        0                 1        0                   0
##  [11,]       1       0        1                 0        1                   1
##  [12,]       1       1        1                 1        1                   1
##  [13,]       1       0        0                 0        0                   1
##  [14,]       1       1        1                 1        1                   1
##  [15,]       0       1        1                 1        1                   0
##  [16,]       1       1        1                 0        1                   1
##  [17,]       0       1        1                 1        1                   1
##  [18,]       0       0        0                 1        0                   0
##  [19,]       1       0        0                 0        1                   1
##  [20,]       1       0        0                 0        0                   1
##  [21,]       1       0        0                 0        0                   1
##  [22,]       0       1        1                 0        1                   0
##  [23,]       1       1        0                 0        0                   1
##  [24,]       1       1        1                 1        1                   1
##  [25,]       0       1        1                 1        1                   0
##  [26,]       1       0        1                 1        1                   1
##  [27,]       1       1        0                 1        0                   1
##  [28,]       1       0        1                 0        1                   1
##  [29,]       0       0        1                 1        0                   1
##  [30,]       1       0        1                 1        1                   1
##  [31,]       0       0        0                 0        0                   1
##  [32,]       0       1        1                 1        0                   1
##  [33,]       0       0        0                 0        0                   1
##  [34,]       0       0        0                 0        0                   1
##  [35,]       0       0        0                 0        0                   0
##  [36,]       0       0        0                 0        0                   1
##  [37,]       0       0        1                 0        1                   1
##  [38,]       0       0        1                 0        0                   1
##  [39,]       0       0        1                 0        0                   1
##  [40,]       0       1        1                 1        1                   0
##  [41,]       1       1        0                 1        1                   1
##  [42,]       1       1        1                 1        0                   0
##  [43,]       1       0        1                 1        0                   0
##  [44,]       1       1        1                 1        0                   1
##  [45,]       0       0        0                 1        1                   0
##  [46,]       1       0        1                 1        1                   1
##  [47,]       0       1        0                 0        1                   1
##  [48,]       1       0        1                 1        1                   0
##  [49,]       1       1        1                 1        0                   1
##  [50,]       0       0        0                 1        0                   0
##  [51,]       1       1        1                 1        0                   0
##  [52,]       1       1        1                 0        0                   1
##  [53,]       1       1        1                 1        1                   0
##  [54,]       1       1        1                 1        1                   1
##  [55,]       1       1        0                 1        1                   0
##  [56,]       0       1        1                 1        1                   0
##  [57,]       1       0        0                 0        1                   1
##  [58,]       0       1        0                 1        1                   1
##  [59,]       1       0        1                 0        0                   1
##  [60,]       1       1        0                 1        1                   1
##  [61,]       1       1        1                 1        1                   0
##  [62,]       0       0        0                 0        1                   0
##  [63,]       1       1        1                 1        1                   0
##  [64,]       0       1        1                 1        0                   0
##  [65,]       1       1        1                 1        1                   1
##  [66,]       1       0        1                 0        1                   0
##  [67,]       1       1        1                 0        1                   1
##  [68,]       1       0        1                 1        1                   1
##  [69,]       1       1        0                 0        0                   1
##  [70,]       1       0        1                 0        1                   1
##  [71,]       0       1        0                 1        0                   0
##  [72,]       1       0        1                 0        1                   1
##  [73,]       1       1        1                 1        1                   1
##  [74,]       1       0        0                 0        0                   1
##  [75,]       1       1        1                 1        1                   1
##  [76,]       0       1        1                 1        1                   0
##  [77,]       1       1        1                 0        1                   1
##  [78,]       1       1        1                 1        1                   1
##  [79,]       0       0        0                 1        0                   0
##  [80,]       1       0        0                 0        1                   1
##  [81,]       1       0        0                 0        0                   1
##  [82,]       1       0        0                 0        0                   1
##  [83,]       0       1        1                 1        0                   0
##  [84,]       0       1        0                 1        1                   1
##  [85,]       1       1        0                 1        1                   1
##  [86,]       0       0        1                 1        1                   1
##  [87,]       0       1        0                 1        1                   1
##  [88,]       1       0        1                 0        0                   0
##  [89,]       0       1        0                 1        0                   0
##  [90,]       1       1        1                 1        0                   0
##  [91,]       0       0        1                 1        0                   0
##  [92,]       1       1        0                 0        1                   1
##  [93,]       1       1        1                 1        0                   0
##  [94,]       0       1        1                 1        1                   1
##  [95,]       1       1        0                 1        1                   1
##  [96,]       1       0        0                 0        0                   0
##  [97,]       0       1        0                 1        1                   1
##  [98,]       0       0        0                 1        1                   1
##  [99,]       1       1        0                 0        1                   0
## [100,]       1       1        1                 1        1                   1
## [101,]       0       1        1                 1        1                   0
## [102,]       1       1        1                 0        1                   1
## [103,]       1       1        1                 1        1                   1
## [104,]       0       0        0                 1        0                   0
## [105,]       1       0        0                 0        1                   1
## [106,]       1       0        0                 0        0                   1
## [107,]       1       0        0                 0        0                   1
## [108,]       0       1        1                 1        0                   0
## [109,]       0       1        0                 1        1                   1
## [110,]       1       1        0                 1        0                   1
## [111,]       1       0        1                 1        1                   1
## [112,]       1       1        0                 1        0                   1
## [113,]       1       0        1                 0        1                   1
## [114,]       0       0        0                 1        0                   0
## [115,]       1       0        1                 1        1                   1
## [116,]       1       1        1                 0        1                   1
## [117,]       1       0        1                 1        1                   1
## [118,]       1       1        0                 0        0                   1
## [119,]       1       0        1                 0        1                   1
## [120,]       0       1        0                 1        0                   0
## [121,]       1       0        1                 0        1                   1
## [122,]       1       1        1                 1        1                   1
## [123,]       1       0        0                 0        0                   1
## [124,]       1       1        1                 1        1                   1
## [125,]       0       1        0                 1        1                   0
## [126,]       1       1        0                 0        1                   1
## [127,]       1       0        1                 1        1                   1
## [128,]       0       0        0                 1        0                   0
## [129,]       1       0        0                 0        1                   1
## [130,]       1       0        0                 0        0                   1
## [131,]       1       0        0                 0        0                   1
## [132,]       0       1        1                 0        1                   0
## [133,]       1       1        0                 0        0                   1
## [134,]       1       1        1                 1        1                   1
## [135,]       0       1        1                 1        1                   0
## [136,]       1       0        1                 1        1                   1
## [137,]       1       1        0                 0        0                   1
## [138,]       1       0        1                 0        1                   1
## [139,]       0       0        1                 1        0                   1
## [140,]       1       0        1                 1        1                   1
## [141,]       1       1        1                 0        1                   1
## [142,]       1       0        1                 1        1                   1
## [143,]       1       1        0                 0        0                   1
## [144,]       1       1        1                 0        1                   1
## [145,]       0       1        0                 1        0                   0
## [146,]       1       0        1                 0        1                   1
## [147,]       1       1        1                 1        1                   1
## [148,]       1       0        0                 1        1                   1
## [149,]       1       1        1                 1        1                   1
## [150,]       0       1        1                 1        1                   0
## [151,]       1       1        0                 1        1                   1
## [152,]       1       1        1                 1        0                   0
## [153,]       1       0        1                 1        0                   0
## [154,]       0       0        0                 0        0                   0
## [155,]       0       0        0                 0        0                   0
## [156,]       0       0        0                 0        0                   0
## [157,]       0       0        0                 0        0                   0
## [158,]       0       0        0                 0        0                   0
## [159,]       1       1        1                 1        0                   1
## [160,]       0       0        0                 1        0                   0
## [161,]       1       1        1                 1        0                   0
## [162,]       1       1        1                 0        0                   1
## [163,]       1       1        1                 1        1                   0
## [164,]       1       1        1                 1        1                   1
## [165,]       1       1        0                 1        1                   0
## [166,]       0       1        1                 1        1                   0
## [167,]       1       0        0                 0        1                   1
## [168,]       0       1        0                 1        1                   1
## [169,]       1       0        1                 0        0                   1
## [170,]       1       1        0                 1        1                   1
## [171,]       1       1        1                 1        1                   0
## [172,]       0       0        0                 0        1                   0
## [173,]       1       1        1                 1        1                   0
## [174,]       0       1        1                 1        0                   0
## [175,]       1       1        1                 1        1                   1
## [176,]       1       0        1                 0        1                   0
## [177,]       1       1        1                 0        1                   1
## [178,]       1       0        1                 1        1                   1
## [179,]       1       1        0                 0        0                   1
## [180,]       1       0        1                 0        1                   1
## [181,]       0       1        0                 1        0                   0
## [182,]       1       0        1                 0        1                   1
## [183,]       1       1        1                 1        1                   1
## [184,]       1       0        0                 0        0                   1
## [185,]       1       1        1                 1        1                   1
## [186,]       0       1        1                 1        1                   0
## [187,]       1       0        0                 0        0                   0
## [188,]       1       0        0                 0        0                   0
## [189,]       0       0        0                 0        0                   0
## [190,]       1       0        0                 0        0                   0
## [191,]       1       0        0                 0        0                   0
## [192,]       1       0        0                 0        0                   0
## [193,]       0       0        0                 0        0                   0
## [194,]       0       0        0                 0        0                   0
## [195,]       1       1        0                 1        1                   1
## [196,]       0       0        1                 1        1                   1
## [197,]       0       1        0                 1        1                   1
## [198,]       1       0        1                 0        0                   0
## [199,]       0       1        0                 1        0                   0
## [200,]       1       1        1                 1        0                   0
## [201,]       0       0        1                 1        0                   0
## [202,]       1       1        0                 0        1                   1
## [203,]       1       1        1                 1        0                   0
## [204,]       0       1        1                 1        1                   1
## [205,]       1       1        0                 1        1                   1
## [206,]       1       0        0                 0        0                   0
## [207,]       0       1        0                 1        1                   1
## [208,]       0       0        0                 0        1                   1
## [209,]       1       1        0                 0        1                   0
## [210,]       1       1        1                 1        1                   1
## [211,]       0       1        1                 1        1                   0
## [212,]       1       1        1                 0        1                   1
## [213,]       1       1        1                 1        1                   1
## [214,]       0       0        0                 1        0                   0
## [215,]       1       0        0                 0        1                   1
## [216,]       1       0        0                 0        0                   1
## [217,]       1       0        0                 0        0                   1
## [218,]       0       1        1                 1        0                   0
## [219,]       0       1        0                 1        1                   1
## [220,]       1       1        0                 1        1                   1
## [221,]       1       1        1                 1        0                   1
## [222,]       0       0        0                 1        0                   0
## [223,]       1       1        1                 1        0                   0
## [224,]       1       1        1                 0        0                   1
## [225,]       1       1        1                 1        1                   0
## [226,]       1       1        1                 1        1                   1
## [227,]       1       1        0                 1        1                   0
## [228,]       0       1        1                 1        1                   0
## [229,]       1       0        0                 0        1                   1
## [230,]       0       1        0                 1        1                   1
## [231,]       1       0        1                 0        0                   1
## [232,]       1       1        0                 1        1                   1
## [233,]       1       1        1                 1        1                   0
## [234,]       0       0        0                 0        1                   0
## [235,]       1       1        1                 1        1                   0
## [236,]       0       1        1                 1        0                   0
## [237,]       1       1        1                 1        1                   1
## [238,]       1       0        1                 0        1                   0
## [239,]       1       1        1                 0        1                   1
## [240,]       0       1        1                 0        1                   0
## [241,]       0       1        0                 0        0                   1
## [242,]       1       1        1                 1        1                   1
## [243,]       0       1        1                 0        0                   0
## [244,]       1       0        1                 1        1                   1
## [245,]       1       1        0                 0        0                   1
## [246,]       1       0        1                 0        0                   1
## [247,]       0       0        1                 1        0                   1
## [248,]       1       0        1                 1        1                   1
## [249,]       1       1        1                 0        1                   1
## [250,]       1       0        0                 0        0                   0
## [251,]       1       1        0                 0        0                   1
## [252,]       1       1        1                 0        1                   1
## [253,]       0       1        0                 1        0                   0
## [254,]       1       0        1                 0        1                   1
## [255,]       1       1        1                 1        1                   1
## [256,]       1       0        0                 1        1                   1
## [257,]       1       1        1                 1        1                   1
## [258,]       0       1        1                 1        1                   0
## [259,]       1       1        0                 1        1                   1
## [260,]       1       1        1                 1        0                   0
## [261,]       1       0        1                 1        0                   0
## [262,]       1       1        1                 1        0                   1
## [263,]       0       0        1                 0        1                   1
## [264,]       1       1        1                 0        1                   1
## [265,]       1       0        1                 1        1                   1
## [266,]       1       1        0                 0        0                   1
## [267,]       1       0        0                 0        0                   0
## [268,]       0       1        0                 1        0                   0
## [269,]       1       0        1                 0        1                   1
## [270,]       1       1        1                 1        1                   1
## [271,]       1       0        0                 0        0                   1
## [272,]       1       1        1                 1        1                   1
## [273,]       0       1        1                 1        1                   0
## [274,]       1       1        1                 0        1                   1
## [275,]       0       1        1                 1        1                   1
## [276,]       0       0        0                 1        0                   0
## [277,]       1       0        0                 0        1                   1
## [278,]       1       0        0                 0        0                   1
## [279,]       1       0        0                 0        0                   1
## [280,]       0       1        1                 0        1                   0
## [281,]       1       1        0                 0        0                   1
## [282,]       1       1        0                 0        0                   1
## [283,]       0       0        0                 0        0                   0
## [284,]       1       0        1                 1        1                   1
## [285,]       0       0        0                 1        0                   0
## [286,]       1       0        0                 0        1                   1
## [287,]       1       0        0                 0        0                   1
## [288,]       1       0        0                 0        0                   1
## [289,]       0       1        1                 0        1                   0
## [290,]       1       1        0                 0        0                   1
## [291,]       1       1        1                 1        1                   1
## [292,]       0       1        1                 1        1                   0
## [293,]       1       0        1                 1        1                   1
## [294,]       1       1        0                 0        0                   1
## [295,]       1       0        1                 0        1                   1
## [296,]       0       0        1                 1        0                   1
## [297,]       1       0        1                 1        1                   1
## [298,]       1       1        1                 0        1                   1
## [299,]       1       0        1                 1        1                   1
## [300,]       1       1        0                 0        0                   1
## [301,]       1       1        1                 0        1                   1
## [302,]       0       1        0                 1        0                   0
## [303,]       1       0        1                 0        1                   1
## [304,]       1       1        1                 1        1                   1
## [305,]       1       0        0                 1        1                   1
## [306,]       1       1        1                 1        1                   1
## [307,]       0       1        1                 1        1                   0
## [308,]       1       1        0                 1        1                   1
## [309,]       1       1        1                 1        0                   0
##        SWALLOWING_DIFFICULTY CHEST_PAIN    WEIGHT HEIGHT_INCH
##   [1,]                     1          1 112.99250    65.78331
##   [2,]                     1          1 136.48730    71.51521
##   [3,]                     0          1 153.02690    69.39874
##   [4,]                     1          1 142.33540    68.21660
##   [5,]                     0          0 144.29710    67.78781
##   [6,]                     0          0 123.30240    68.69784
##   [7,]                     0          1 141.49470    69.80204
##   [8,]                     1          0 136.46230    70.01472
##   [9,]                     0          0 112.37230    67.90265
##  [10,]                     1          1 120.66720    66.78236
##  [11,]                     1          0 127.45160    66.48769
##  [12,]                     0          1 114.14300    67.62333
##  [13,]                     0          0 125.61070    68.30248
##  [14,]                     0          1 122.46180    67.11656
##  [15,]                     0          1 116.08660    68.27967
##  [16,]                     1          0 139.99750    71.09160
##  [17,]                     0          1 129.50230    66.46100
##  [18,]                     1          1 142.97330    68.64927
##  [19,]                     0          0 137.90250    71.23033
##  [20,]                     0          0 124.04490    67.13118
##  [21,]                     1          0 141.28070    67.83379
##  [22,]                     1          0 143.53920    68.87881
##  [23,]                     0          0  97.90191    63.48115
##  [24,]                     0          1 129.50270    68.42187
##  [25,]                     1          1 141.85010    67.62804
##  [26,]                     1          1 129.72440    67.20864
##  [27,]                     1          1 142.42350    70.84235
##  [28,]                     0          1 131.55020    67.49434
##  [29,]                     1          1 108.33240    66.53401
##  [30,]                     0          0 113.89220    65.44098
##  [31,]                     0          0 103.30160    69.52330
##  [32,]                     1          1 120.75360    65.81320
##  [33,]                     1          0 125.78860    67.81630
##  [34,]                     1          1 136.22250    70.59505
##  [35,]                     1          1 140.10150    71.80484
##  [36,]                     1          0 128.74870    69.20613
##  [37,]                     0          1 141.79940    66.80368
##  [38,]                     1          0 121.23190    67.65893
##  [39,]                     0          1 131.34780    67.80701
##  [40,]                     0          1 106.71150    64.04535
##  [41,]                     0          1 124.35980    68.57463
##  [42,]                     1          0 124.85910    65.18357
##  [43,]                     0          0 139.67110    69.65814
##  [44,]                     0          1 137.36960    67.96731
##  [45,]                     1          0 106.44990    65.98088
##  [46,]                     1          1 128.76390    68.67249
##  [47,]                     1          1 145.68370    66.88088
##  [48,]                     1          1 116.81900    67.69868
##  [49,]                     1          1 143.62150    69.82117
##  [50,]                     0          0 134.93250    69.08817
##  [51,]                     0          1 147.02190    69.91479
##  [52,]                     0          0 126.32850    67.33182
##  [53,]                     1          1 125.48390    70.26939
##  [54,]                     1          1 115.70840    69.10344
##  [55,]                     0          0 123.48920    65.38356
##  [56,]                     1          0 147.89260    70.18447
##  [57,]                     0          1 155.89870    70.40617
##  [58,]                     1          1 128.07420    66.54376
##  [59,]                     1          1 119.37010    66.36418
##  [60,]                     0          1 133.81480    67.53700
##  [61,]                     1          1 128.73250    66.50418
##  [62,]                     0          0 137.54530    68.99958
##  [63,]                     0          0 129.76040    68.30355
##  [64,]                     1          0 128.82400    67.01255
##  [65,]                     0          1 135.31650    70.80592
##  [66,]                     1          1 109.61130    68.21951
##  [67,]                     0          1 142.46840    69.05914
##  [68,]                     0          0 132.74900    67.73103
##  [69,]                     1          1 103.52750    67.21568
##  [70,]                     1          0 124.72990    67.36763
##  [71,]                     1          1 129.31370    65.27033
##  [72,]                     1          0 134.01750    70.84278
##  [73,]                     0          1 140.39690    69.92442
##  [74,]                     0          0 102.83510    64.28508
##  [75,]                     0          1 128.52140    68.24520
##  [76,]                     0          0 120.29910    66.35708
##  [77,]                     1          1 138.60360    68.36275
##  [78,]                     0          1 132.95740    65.47690
##  [79,]                     1          1 115.62330    69.71947
##  [80,]                     1          1 122.52400    67.72554
##  [81,]                     0          0 134.62540    68.63941
##  [82,]                     1          0 121.89860    66.78405
##  [83,]                     1          1 155.37670    70.05147
##  [84,]                     0          0 128.94180    66.27848
##  [85,]                     0          1 129.10130    69.20198
##  [86,]                     1          0 139.47330    69.13481
##  [87,]                     0          1 140.89010    67.36436
##  [88,]                     1          1 131.59160    70.09297
##  [89,]                     0          0 121.12320    70.17660
##  [90,]                     1          1 131.51270    68.22556
##  [91,]                     1          1 136.54790    68.12932
##  [92,]                     0          1 141.48960    70.24256
##  [93,]                     1          1 140.61040    71.48752
##  [94,]                     1          0 112.14130    69.20477
##  [95,]                     1          1 133.45700    70.06306
##  [96,]                     1          1 131.80010    70.55703
##  [97,]                     0          1 120.02850    66.28644
##  [98,]                     0          0 123.09720    63.42577
##  [99,]                     1          0 128.14320    66.76711
## [100,]                     0          1 115.47590    68.88741
## [101,]                     0          0 102.09270    64.87434
## [102,]                     1          1 130.35300    67.09272
## [103,]                     0          1 134.18420    68.34761
## [104,]                     1          1  98.64133    65.61073
## [105,]                     1          1 114.55990    67.75551
## [106,]                     0          0 123.49170    68.02120
## [107,]                     1          0 123.04800    67.66193
## [108,]                     1          1 126.47720    66.31460
## [109,]                     0          0 128.41700    69.43706
## [110,]                     0          1 127.19410    63.83624
## [111,]                     1          1 122.05620    67.72277
## [112,]                     1          1 127.60640    70.05098
## [113,]                     0          1 131.64230    70.18602
## [114,]                     1          1 111.89550    65.94588
## [115,]                     0          0 122.03900    70.00700
## [116,]                     0          0 128.55470    68.61129
## [117,]                     0          1 132.67920    68.80817
## [118,]                     1          0 136.06320    69.76212
## [119,]                     1          0 115.94030    65.45539
## [120,]                     1          1 136.90410    68.82534
## [121,]                     1          0 119.88040    65.80030
## [122,]                     0          1 109.00550    67.21474
## [123,]                     0          0 128.27050    69.42021
## [124,]                     0          0 135.29130    68.94396
## [125,]                     0          1 106.85580    67.94150
## [126,]                     0          0 123.29390    65.62506
## [127,]                     0          1 109.51430    66.49607
## [128,]                     1          1 119.30870    67.92809
## [129,]                     1          0 140.24020    68.89415
## [130,]                     0          0 133.98410    70.24100
## [131,]                     1          0 132.58070    68.26623
## [132,]                     1          0 130.69880    71.23161
## [133,]                     0          0 115.56370    69.09747
## [134,]                     0          1 123.79410    64.39693
## [135,]                     1          1 128.14270    71.09585
## [136,]                     1          0 135.96460    68.21868
## [137,]                     0          1 116.62730    65.91721
## [138,]                     0          1 126.82410    67.43690
## [139,]                     1          1 151.39130    73.90107
## [140,]                     0          0 130.40220    69.98149
## [141,]                     0          0 136.20680    69.51862
## [142,]                     0          1 113.39890    65.18437
## [143,]                     1          0 125.32870    68.00869
## [144,]                     1          1 127.58460    68.33840
## [145,]                     1          1 107.15640    65.18417
## [146,]                     1          0 116.45880    68.26209
## [147,]                     0          1 133.84020    68.56865
## [148,]                     1          0 112.89010    64.49675
## [149,]                     0          1 130.75680    68.71053
## [150,]                     0          1 137.75710    68.89148
## [151,]                     0          1 125.40360    69.54011
## [152,]                     1          0 138.46590    67.39964
## [153,]                     0          0 120.81840    66.47521
## [154,]                     0          1 140.15390    66.01217
## [155,]                     0          0 136.73970    72.44434
## [156,]                     0          1 106.11390    64.12642
## [157,]                     0          1 158.95620    70.98112
## [158,]                     0          1 108.78680    67.50124
## [159,]                     1          1 138.77580    72.01515
## [160,]                     0          0 115.91360    65.31143
## [161,]                     0          1 146.29220    67.07509
## [162,]                     0          0 109.87650    64.39148
## [163,]                     1          1 139.04990    69.37003
## [164,]                     1          1 119.90010    68.37921
## [165,]                     0          0 128.30690    65.31018
## [166,]                     1          0 127.24280    67.13690
## [167,]                     0          1 115.23060    68.39468
## [168,]                     1          1 124.79750    66.29180
## [169,]                     1          1 126.95110    67.18660
## [170,]                     0          1 111.27110    65.99156
## [171,]                     1          1 122.60890    69.43393
## [172,]                     0          0 124.20840    67.97463
## [173,]                     0          0 124.64530    67.76133
## [174,]                     1          0 119.51690    65.27864
## [175,]                     0          1 139.29830    73.83364
## [176,]                     1          1 104.82650    66.81312
## [177,]                     0          1 123.04240    66.89411
## [178,]                     0          0 118.89230    65.73568
## [179,]                     1          1 121.49390    65.98283
## [180,]                     1          0 119.24880    66.58396
## [181,]                     1          1 135.02390    67.11294
## [182,]                     1          0 116.22800    65.87481
## [183,]                     0          1 109.17310    66.78067
## [184,]                     0          0 124.22370    68.73577
## [185,]                     0          1 141.16450    66.22666
## [186,]                     0          0 129.15010    65.95968
## [187,]                     0          0 127.86930    68.58372
## [188,]                     0          0 120.92440    66.59347
## [189,]                     0          0 127.64660    66.96574
## [190,]                     0          0 101.46930    68.08015
## [191,]                     0          0 144.99270    70.19025
## [192,]                     0          0 110.95230    65.52149
## [193,]                     0          0 132.86250    67.45905
## [194,]                     0          0 146.33850    67.40985
## [195,]                     0          1 145.58940    69.66158
## [196,]                     1          0 120.84310    65.79799
## [197,]                     0          1 115.78130    66.10558
## [198,]                     1          1 128.30190    68.23987
## [199,]                     0          0 127.47180    68.02403
## [200,]                     1          1 127.87610    71.39044
## [201,]                     1          1 121.49970    65.73160
## [202,]                     0          1 112.71480    66.43358
## [203,]                     1          1 135.00200    70.01309
## [204,]                     1          0 128.67890    69.48146
## [205,]                     1          1 124.40620    68.62764
## [206,]                     1          1 140.02600    68.36275
## [207,]                     0          1 117.51900    68.39028
## [208,]                     0          0 143.87370    68.77413
## [209,]                     1          0 141.17030    69.92360
## [210,]                     0          1 155.94140    71.55542
## [211,]                     0          0 134.00930    68.44764
## [212,]                     1          1 130.09750    66.71398
## [213,]                     0          1 106.22650    66.68413
## [214,]                     1          1 112.04890    67.93699
## [215,]                     1          1 136.18840    68.89855
## [216,]                     0          0 131.23600    67.29191
## [217,]                     1          0 131.32310    69.57212
## [218,]                     1          1 119.52610    67.67479
## [219,]                     0          0 116.99650    69.04155
## [220,]                     0          1 138.52550    67.96765
## [221,]                     1          1 109.65180    65.83982
## [222,]                     0          0 130.15690    65.77288
## [223,]                     0          1 137.11140    71.14106
## [224,]                     0          0 113.75900    67.83055
## [225,]                     1          1 114.97250    65.06930
## [226,]                     1          1 127.71490    69.70745
## [227,]                     0          0 121.99720    69.92983
## [228,]                     1          0 117.96070    66.11569
## [229,]                     0          1 127.71410    68.61364
## [230,]                     1          1 117.96190    68.99760
## [231,]                     1          1 125.15540    66.79171
## [232,]                     0          1 141.10260    68.02363
## [233,]                     1          1 145.48220    69.67258
## [234,]                     0          0 116.06500    71.82178
## [235,]                     0          0 135.74580    72.74676
## [236,]                     1          0 132.92480    67.27951
## [237,]                     0          1 115.66220    67.41015
## [238,]                     1          1 114.31840    68.53150
## [239,]                     0          1 148.95200    68.47126
## [240,]                     1          0 142.18780    68.51867
## [241,]                     0          0 134.10400    63.72529
## [242,]                     0          1 141.89260    67.70483
## [243,]                     1          1 138.74440    69.47115
## [244,]                     1          0 134.44900    66.70198
## [245,]                     0          1 117.01670    65.23126
## [246,]                     0          1 115.67520    69.89473
## [247,]                     1          1 134.79050    69.83048
## [248,]                     0          0 120.57460    65.39790
## [249,]                     0          0 120.08350    68.32214
## [250,]                     0          0  84.35980    65.93895
## [251,]                     1          0 138.93940    70.09805
## [252,]                     1          1 143.52450    66.05531
## [253,]                     1          1 123.13470    68.23481
## [254,]                     1          0 115.52610    65.21758
## [255,]                     0          1 120.98440    69.16173
## [256,]                     1          0 120.64730    67.60064
## [257,]                     0          1 124.03520    67.28621
## [258,]                     0          1 117.22380    66.84323
## [259,]                     0          1 127.95980    68.08281
## [260,]                     1          0 116.75270    66.56991
## [261,]                     0          0 121.99570    70.16973
## [262,]                     0          1 123.99520    67.85113
## [263,]                     0          0 108.85500    66.62309
## [264,]                     0          0 104.65740    63.68816
## [265,]                     0          1 132.24800    68.03560
## [266,]                     1          0 127.18340    66.94100
## [267,]                     0          0 125.12090    66.26292
## [268,]                     1          1 133.32200    70.73010
## [269,]                     1          0 122.33640    70.70844
## [270,]                     0          1 130.26360    73.26872
## [271,]                     0          0 116.74310    63.79021
## [272,]                     0          1 125.85340    67.84109
## [273,]                     0          1 100.62700    67.78058
## [274,]                     1          0 118.49450    67.23901
## [275,]                     0          1 137.12550    66.75701
## [276,]                     1          1 118.69910    69.03098
## [277,]                     0          0 124.16410    68.52652
## [278,]                     0          0 124.94420    64.65419
## [279,]                     1          0 126.38890    65.14295
## [280,]                     1          0 121.52550    66.74124
## [281,]                     0          0 133.29510    66.99923
## [282,]                     0          1 127.40720    70.26611
## [283,]                     1          1 125.08000    67.57666
## [284,]                     1          1 102.81140    66.30582
## [285,]                     1          1 134.22120    68.90702
## [286,]                     1          0 100.97580    65.60543
## [287,]                     0          0 145.88860    68.00189
## [288,]                     1          0 155.30460    69.93715
## [289,]                     1          0 138.71750    70.14590
## [290,]                     0          0 116.26110    66.66364
## [291,]                     0          1 120.60870    69.40676
## [292,]                     1          1 114.40830    66.80598
## [293,]                     1          0 133.34060    67.70048
## [294,]                     0          1  92.74955    69.13438
## [295,]                     0          1 131.78250    67.53769
## [296,]                     1          1 118.38650    65.77912
## [297,]                     0          0 131.14660    66.25769
## [298,]                     0          0 130.20330    67.39038
## [299,]                     0          1 129.18360    64.94327
## [300,]                     1          0 143.14450    69.25699
## [301,]                     1          1 138.73070    69.07739
## [302,]                     1          1 130.95280    69.64403
## [303,]                     1          0 124.30320    69.07705
## [304,]                     0          1 135.37020    68.01304
## [305,]                     1          0 124.19880    68.85664
## [306,]                     0          1 111.23890    63.19158
## [307,]                     0          1 129.40370    65.57591
## [308,]                     0          1 127.74440    69.12101
## [309,]                     1          0 121.33110    69.78765
drop(scale(new_cancer,center=center, scale=scale)%*%cancer_pca$rotation[,1])
##   [1] -0.646329947 -0.610508061 -0.749550736  1.096019632  0.036188930
##   [6] -0.532567242 -2.543550172  2.572207921  1.272938608  1.396823254
##  [11]  2.064989024 -3.094017924  0.217887666 -3.138457875 -2.644849262
##  [16]  1.650628200 -2.832351242  1.926614145  2.058726013  0.277622753
##  [21]  3.229605844  1.856494117 -0.050480044 -3.114648178  0.277610744
##  [26] -0.593103049  0.798726715 -1.483179713  1.135171580 -1.513992882
##  [31]  1.249804903 -1.015659657  1.959456710  2.332965976  1.785139801
##  [36]  2.803119610 -0.906183428  0.625607571 -0.980782008 -2.531034433
##  [41] -1.849943675 -0.768929068  1.593703995 -1.913272210  1.543800949
##  [46]  0.292377930 -0.251600030  0.254838293  0.179367433  0.952911843
##  [51] -0.851848170  0.301087025 -0.906545994 -1.669956979  0.195017025
##  [56]  0.200650077  0.518073225 -1.831824121  0.685756178 -0.498748639
##  [61] -0.851501742  1.671406217 -1.102287719  0.487489582 -1.821523333
##  [66]  1.890194887 -0.908993115 -2.188253111  1.922127515  1.831473258
##  [71]  1.111645609  1.972055116 -3.014541351  0.297544932 -3.123513629
##  [76] -2.175119346  0.988165063 -3.171148404  1.909872378  1.884232732
##  [81]  0.148410514  3.159260208  1.589202745 -0.735262114 -2.492696658
##  [86]  0.164831585 -0.791080564  1.019972886  1.355490521 -0.217694604
##  [91]  0.200980870 -1.224091912 -1.377079915  1.105509567 -1.763739245
##  [96]  2.144246653 -0.247301899 -0.943580309  1.434728986 -3.084789560
## [101] -2.211988131  0.934186102 -3.134406710  1.829037095  1.889637650
## [106]  0.304495611  3.150251750  1.504721972 -0.513569276 -2.049787993
## [111] -0.548863117  0.137370850 -0.769133382  1.052948611 -0.832893079
## [116] -0.521560718 -2.590558669  2.565856126  1.890132650  1.809485293
## [121]  1.154753405 -3.068643554  0.603092803 -0.262265717 -2.166676433
## [126]  1.396820173 -2.621538470  1.904628487  2.449232521  0.346806820
## [131]  3.029389183  1.929414827 -0.087138867 -3.286936885 -0.243063096
## [136] -0.885383059  0.779845934 -1.475619881  1.315156524 -1.435594309
## [141]  0.311554205 -1.898169897  1.817982682  1.132188201  1.041211639
## [146]  1.911956582 -2.208254898  0.199618587 -3.151824202 -2.581152399
## [151] -1.821212050 -0.709027954  1.527353442  0.134446169  2.379419131
## [156]  1.816004356  0.693446059  1.637082331  0.296933463  0.822754284
## [161] -0.918911402  0.231900961 -1.013939681 -1.772694007  0.113097963
## [166]  0.075576812  0.477358107 -1.789229364  0.719595969 -0.479345237
## [171] -0.706487604  1.659264316 -1.053631487  0.439619994 -1.736485551
## [176]  1.908193822 -1.025193951 -2.229264288  1.957225328  1.838526733
## [181]  1.180112751  1.811861750 -3.110670459  0.360229263 -3.223541067
## [186] -2.269746579  2.747577269 -0.149697264  2.400777592  2.664155409
## [191]  0.613534144  2.833005133  3.117056920  1.396552964 -2.512642306
## [196]  0.041302770 -0.813244847  0.986709032  1.252252204 -0.137885258
## [201]  0.136542296 -1.270419897 -1.511779573  1.085397022 -1.937338444
## [206]  2.079880884 -0.238660237 -0.159651843  1.500566250 -3.014209221
## [211] -2.105058072  0.942418911 -3.148924082  1.878394695  1.966715740
## [216]  0.277041266  3.171498795  1.556928786 -0.616500433 -2.586211894
## [221]  0.137716815  0.865093182 -0.913971012  0.313977949 -1.072776501
## [226] -1.699472023  0.251825578  0.014567830  0.504752774 -1.698692239
## [231]  0.558690456 -0.464475998 -0.736607022  1.791907070 -1.021622690
## [236]  0.511871527 -1.857682768  1.973432877 -0.844025398  1.798603632
## [241]  0.567970913 -3.128591618  0.921300172 -0.707766669  0.727027732
## [246] -0.813209418  1.137562086 -1.568549443  0.206337661  0.582400965
## [251]  1.852485410  1.069824793  1.320083419  1.826416008 -2.295131492
## [256]  0.184324517 -3.143108851 -2.658851944 -1.871308247 -0.711591973
## [261]  1.686997211 -1.858110215 -0.009983675 -0.640492349 -2.667743902
## [266]  2.455060778  1.289042304  1.464834078  2.198079582 -2.876746306
## [271]  0.060055521 -3.142504794 -2.634807935  1.505301199 -2.740709424
## [276]  1.905774831  2.017633169  0.099735552  3.015656624  1.825438683
## [281] -0.131569292 -1.322834911  1.736775731 -0.592930367  1.928894090
## [286]  2.367428208  0.290098251  3.070879292  1.901858849 -0.148458186
## [291] -3.160670480 -0.350752444 -0.898366238  0.861502720 -1.473211209
## [296]  1.111453285 -1.529405423  0.258107397 -1.904656129  1.848956846
## [301]  1.150509115  1.152918867  1.932277477 -2.222289178  0.309135098
## [306] -3.290318919 -2.664442991 -1.831829290 -0.648431973
predict(cancer_pca)[,1]
##   [1] -0.646329947 -0.610508061 -0.749550736  1.096019632  0.036188930
##   [6] -0.532567242 -2.543550172  2.572207921  1.272938608  1.396823254
##  [11]  2.064989024 -3.094017924  0.217887666 -3.138457875 -2.644849262
##  [16]  1.650628200 -2.832351242  1.926614145  2.058726013  0.277622753
##  [21]  3.229605844  1.856494117 -0.050480044 -3.114648178  0.277610744
##  [26] -0.593103049  0.798726715 -1.483179713  1.135171580 -1.513992882
##  [31]  1.249804903 -1.015659657  1.959456710  2.332965976  1.785139801
##  [36]  2.803119610 -0.906183428  0.625607571 -0.980782008 -2.531034433
##  [41] -1.849943675 -0.768929068  1.593703995 -1.913272210  1.543800949
##  [46]  0.292377930 -0.251600030  0.254838293  0.179367433  0.952911843
##  [51] -0.851848170  0.301087025 -0.906545994 -1.669956979  0.195017025
##  [56]  0.200650077  0.518073225 -1.831824121  0.685756178 -0.498748639
##  [61] -0.851501742  1.671406217 -1.102287719  0.487489582 -1.821523333
##  [66]  1.890194887 -0.908993115 -2.188253111  1.922127515  1.831473258
##  [71]  1.111645609  1.972055116 -3.014541351  0.297544932 -3.123513629
##  [76] -2.175119346  0.988165063 -3.171148404  1.909872378  1.884232732
##  [81]  0.148410514  3.159260208  1.589202745 -0.735262114 -2.492696658
##  [86]  0.164831585 -0.791080564  1.019972886  1.355490521 -0.217694604
##  [91]  0.200980870 -1.224091912 -1.377079915  1.105509567 -1.763739245
##  [96]  2.144246653 -0.247301899 -0.943580309  1.434728986 -3.084789560
## [101] -2.211988131  0.934186102 -3.134406710  1.829037095  1.889637650
## [106]  0.304495611  3.150251750  1.504721972 -0.513569276 -2.049787993
## [111] -0.548863117  0.137370850 -0.769133382  1.052948611 -0.832893079
## [116] -0.521560718 -2.590558669  2.565856126  1.890132650  1.809485293
## [121]  1.154753405 -3.068643554  0.603092803 -0.262265717 -2.166676433
## [126]  1.396820173 -2.621538470  1.904628487  2.449232521  0.346806820
## [131]  3.029389183  1.929414827 -0.087138867 -3.286936885 -0.243063096
## [136] -0.885383059  0.779845934 -1.475619881  1.315156524 -1.435594309
## [141]  0.311554205 -1.898169897  1.817982682  1.132188201  1.041211639
## [146]  1.911956582 -2.208254898  0.199618587 -3.151824202 -2.581152399
## [151] -1.821212050 -0.709027954  1.527353442  0.134446169  2.379419131
## [156]  1.816004356  0.693446059  1.637082331  0.296933463  0.822754284
## [161] -0.918911402  0.231900961 -1.013939681 -1.772694007  0.113097963
## [166]  0.075576812  0.477358107 -1.789229364  0.719595969 -0.479345237
## [171] -0.706487604  1.659264316 -1.053631487  0.439619994 -1.736485551
## [176]  1.908193822 -1.025193951 -2.229264288  1.957225328  1.838526733
## [181]  1.180112751  1.811861750 -3.110670459  0.360229263 -3.223541067
## [186] -2.269746579  2.747577269 -0.149697264  2.400777592  2.664155409
## [191]  0.613534144  2.833005133  3.117056920  1.396552964 -2.512642306
## [196]  0.041302770 -0.813244847  0.986709032  1.252252204 -0.137885258
## [201]  0.136542296 -1.270419897 -1.511779573  1.085397022 -1.937338444
## [206]  2.079880884 -0.238660237 -0.159651843  1.500566250 -3.014209221
## [211] -2.105058072  0.942418911 -3.148924082  1.878394695  1.966715740
## [216]  0.277041266  3.171498795  1.556928786 -0.616500433 -2.586211894
## [221]  0.137716815  0.865093182 -0.913971012  0.313977949 -1.072776501
## [226] -1.699472023  0.251825578  0.014567830  0.504752774 -1.698692239
## [231]  0.558690456 -0.464475998 -0.736607022  1.791907070 -1.021622690
## [236]  0.511871527 -1.857682768  1.973432877 -0.844025398  1.798603632
## [241]  0.567970913 -3.128591618  0.921300172 -0.707766669  0.727027732
## [246] -0.813209418  1.137562086 -1.568549443  0.206337661  0.582400965
## [251]  1.852485410  1.069824793  1.320083419  1.826416008 -2.295131492
## [256]  0.184324517 -3.143108851 -2.658851944 -1.871308247 -0.711591973
## [261]  1.686997211 -1.858110215 -0.009983675 -0.640492349 -2.667743902
## [266]  2.455060778  1.289042304  1.464834078  2.198079582 -2.876746306
## [271]  0.060055521 -3.142504794 -2.634807935  1.505301199 -2.740709424
## [276]  1.905774831  2.017633169  0.099735552  3.015656624  1.825438683
## [281] -0.131569292 -1.322834911  1.736775731 -0.592930367  1.928894090
## [286]  2.367428208  0.290098251  3.070879292  1.901858849 -0.148458186
## [291] -3.160670480 -0.350752444 -0.898366238  0.861502720 -1.473211209
## [296]  1.111453285 -1.529405423  0.258107397 -1.904656129  1.848956846
## [301]  1.150509115  1.152918867  1.932277477 -2.222289178  0.309135098
## [306] -3.290318919 -2.664442991 -1.831829290 -0.648431973
#The aboved two gives us the same thing. predict is a good function to know.
cancer$LUNG_CANCER <- as.factor(cancer$LUNG_CANCER)
out <- sapply(1:5, function(i){plot(cancer$LUNG_CANCER,cancer_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="LUNG CANCER")})

library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(FactoMineR)
library(ggfortify)
library(psych)
## 
## Attaching package: 'psych'
## 
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
library(corrplot)
## corrplot 0.92 loaded
library(devtools)
## Loading required package: usethis
fviz_eig(cancer_pca, addlabels = TRUE)

# In this scree plot, we will consider the first 7 PC's as it explains almost 70% of the variance in the dataset.
fviz_pca_var(cancer_pca,col.var = "cos2",
             gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
             repel = TRUE)

# The graph is a visualization of the principal components of a PCA analysis. Each point on the plot represents a variable in the original dataset, and the position of the point represents the contribution of the variable to the principal components. The size of the point represents the variability explained by the variable, and the color represents the squared cosine of the variable, which indicates the correlation between the variable and the principal component. The gradient of colors indicates the strength of the correlation, with darker colors indicating stronger correlation. From this graph, we can identify which variables are most important in explaining the variation in the data, and which variables are most strongly correlated with each principal component.Here, alcohol consumption, swallowing difficulty, anxiety, yellow fingers, chest pain, shortness of breath are some of the variables 

# Different PCA Method. 
res.pca <- PCA(cancer[,-1], graph = FALSE)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 309 individuals, described by 17 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"
# Visualize and Interpret PCA using these functions 

#get_eigenvalue(res.pca): Extract the eigenvalues/variances of principal components
#fviz_eig(res.pca): Visualize the eigenvalues
#get_pca_ind(res.pca), get_pca_var(res.pca): Extract the results for individuals and variables, respectively.
#fviz_pca_ind(res.pca), fviz_pca_var(res.pca): Visualize the results individuals and variables, respectively.
#fviz_pca_biplot(res.pca): Make a biplot of individuals and variables.

eig.val <- get_eigenvalue(res.pca)
eig.val
##        eigenvalue variance.percent cumulative.variance.percent
## Dim.1   2.8645733        16.850431                    16.85043
## Dim.2   1.9575778        11.515164                    28.36559
## Dim.3   1.6886084         9.932991                    38.29859
## Dim.4   1.4725468         8.662040                    46.96063
## Dim.5   1.3035915         7.668185                    54.62881
## Dim.6   1.0719035         6.305315                    60.93413
## Dim.7   0.9543405         5.613767                    66.54789
## Dim.8   0.8911585         5.242109                    71.79000
## Dim.9   0.8156856         4.798150                    76.58815
## Dim.10  0.7144905         4.202885                    80.79104
## Dim.11  0.6332509         3.725005                    84.51604
## Dim.12  0.5858596         3.446233                    87.96228
## Dim.13  0.5307591         3.122113                    91.08439
## Dim.14  0.5162084         3.036520                    94.12091
## Dim.15  0.4035160         2.373623                    96.49453
## Dim.16  0.3189926         1.876427                    98.37096
## Dim.17  0.2769370         1.629041                   100.00000
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 20))

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (nbut not "text")
             col.ind = cancer$LUNG_CANCER, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, # Concentration ellipses
             legend.title = "Groups"
             )

#Each ellipse represents the range of scores for each group in the first two principal components. The center of the ellipse represents the centroid of each group in the first two principal components.If the ellipses of two groups overlap significantly, it means that they have similar scores in the first two principal components, and thus are not easily distinguishable based on those components. On the other hand, if the ellipses of two groups do not overlap, it means that they have different scores in the first two principal components, and thus are easily distinguishable based on those components. In the graph, some part of the ellipse is overlapping while some part isn't. So, some of the scores for PC1 and PC2 are same while some are different. 


res.desc <- dimdesc(res.pca, axes = c(1,2,3,4,5), proba = 0.05)


fviz_pca_biplot(res.pca, 
                # Individuals
                geom.ind = "point",
                fill.ind = cancer$LUNG_CANCER, col.ind = "black",
                pointshape = 21, pointsize = 2,
                palette = "jco",
                addEllipses = TRUE,
                # Variables
                alpha.var ="contrib", col.var = "contrib",
                gradient.cols = "RdYlBu",
                
                legend.title = list(fill = "LUNG CANCER", color = "Contrib",
                                    alpha = "Contrib")
                )

# Here we can underrstand that the closer the variables are to a principal component, the stronger the relationship. Variables that are close together on the biplot are positively correlated, while variables that are far apart are negatively correlated. Here, peer pressure, anxiety, swallowing difficulty, yellow fingers are strongly correlated with each other. Also, chest pain, allergy, wheezing and coughing are correlated to each other. These can be considered as some of the important factors that affect lung cancer.

Logistic Regression

library(ggplot2)
library(readr)
library(cowplot)
#library(regclass)
#library(caret)
library(e1071)
library(pROC)
## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
data <- read_csv("/Users/batul/Desktop/MVA/LUNGCANCER3.csv")
## Rows: 309 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (18): LUNG_CANCER, GENDER, AGE, SMOKING, YELLOW_FINGERS, ANXIETY, PEER_P...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
data$SMOKING <- as.factor(data$SMOKING)
data$YELLOW_FINGERS <- as.factor(data$YELLOW_FINGERS)
data$ANXIETY <- as.factor(data$ANXIETY)
data$PEER_PRESSURE <- as.factor(data$PEER_PRESSURE)
data$FATIGUE <- as.factor(data$FATIGUE)
data$ALLERGY <- as.factor(data$ALLERGY)
data$AGE <- as.integer(data$AGE)
data$WHEEZING <- as.factor(data$WHEEZING)
data$ALCOHOL_CONSUMING <- as.integer(data$ALCOHOL_CONSUMING)
data$COUGHING <- as.factor(data$COUGHING)
data$SHORTNESS_OF_BREATH <- as.factor(data$SHORTNESS_OF_BREATH)
data$SWALLOWING_DIFFICULTY <- as.factor(data$SWALLOWING_DIFFICULTY)
data$CHEST_PAIN <- as.factor(data$CHEST_PAIN)
data$WEIGHT <- as.factor(data$WEIGHT)
data$HEIGHT_INCH <- as.factor(data$HEIGHT_INCH)
data$CHRONIC_DISEASE <- as.factor(data$CHRONIC_DISEASE)


## Exploratory Analysis

xtabs(~ LUNG_CANCER + SMOKING, data=data)
##            SMOKING
## LUNG_CANCER   0   1
##           0  19  20
##           1 155 115
# There are 19 observations that are non-smokers and do not have lung cancer, 20 observations that are non-smokers and have lung cancer, 155 observations that are smokers and do not have lung cancer, and 115 observations that are smokers and have lung cancer. This information can be useful to understand the relationship between smoking and lung cancer and to understand if there is a significant association between the two variables. Similarly, we can get a table for other variables like anxiety, fatigue etc and understand if there is a significant association between those variables. 
xtabs(~ LUNG_CANCER + YELLOW_FINGERS, data=data)
##            YELLOW_FINGERS
## LUNG_CANCER   0   1
##           0  26  13
##           1 107 163
xtabs(~ LUNG_CANCER + ANXIETY, data=data)
##            ANXIETY
## LUNG_CANCER   0   1
##           0  27  12
##           1 128 142
xtabs(~ LUNG_CANCER + PEER_PRESSURE, data=data)
##            PEER_PRESSURE
## LUNG_CANCER   0   1
##           0  29  10
##           1 125 145
xtabs(~ LUNG_CANCER + FATIGUE, data=data)
##            FATIGUE
## LUNG_CANCER   0   1
##           0  20  19
##           1  81 189
xtabs(~ LUNG_CANCER + ALLERGY, data=data)
##            ALLERGY
## LUNG_CANCER   0   1
##           0  34   5
##           1 103 167
xtabs(~ LUNG_CANCER + WHEEZING, data=data)
##            WHEEZING
## LUNG_CANCER   0   1
##           0  30   9
##           1 107 163
xtabs(~ LUNG_CANCER + ALCOHOL_CONSUMING, data=data)
##            ALCOHOL_CONSUMING
## LUNG_CANCER   0   1
##           0  32   7
##           1 105 165
xtabs(~ LUNG_CANCER + COUGHING, data=data)
##            COUGHING
## LUNG_CANCER   0   1
##           0  29  10
##           1 101 169
xtabs(~ LUNG_CANCER + SHORTNESS_OF_BREATH, data=data)
##            SHORTNESS_OF_BREATH
## LUNG_CANCER   0   1
##           0  17  22
##           1  94 176
xtabs(~ LUNG_CANCER + SWALLOWING_DIFFICULTY, data=data)
##            SWALLOWING_DIFFICULTY
## LUNG_CANCER   0   1
##           0  34   5
##           1 130 140
xtabs(~ LUNG_CANCER + CHEST_PAIN, data=data)
##            CHEST_PAIN
## LUNG_CANCER   0   1
##           0  27  12
##           1 110 160
xtabs(~ LUNG_CANCER + CHRONIC_DISEASE, data=data)
##            CHRONIC_DISEASE
## LUNG_CANCER   0   1
##           0  25  14
##           1 128 142
logistic_simple <- glm(LUNG_CANCER ~ SMOKING, data=data, family="binomial")
summary(logistic_simple)
## 
## Call:
## glm(formula = LUNG_CANCER ~ SMOKING, family = "binomial", data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.1046   0.4809   0.4809   0.5663   0.5663  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   2.0990     0.2431   8.636   <2e-16 ***
## SMOKING1     -0.3498     0.3432  -1.019    0.308    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 234.30  on 308  degrees of freedom
## Residual deviance: 233.26  on 307  degrees of freedom
## AIC: 237.26
## 
## Number of Fisher Scoring iterations: 4
#The slope estimate for SMOKING 1 is -0.3498, indicating that for every one-unit increase in SMOKING (i.e., from 0 to 1), the log odds of LUNG_CANCER decreases by 0.3498 units. The p-value for SMOKING 1 is 0.308, which is not statistically significant at the conventional alpha level of 0.05. The residual deviance is 233.26 on 307 degrees of freedom, indicating that the model provides a good fit to the data. The AIC value of 237.26 suggests that this simple logistic model is a good fit for predicting the probability of LUNG CANCER based on SMOKING.

## Lastly, let's  see what this logistic regression predicts, given

predicted.data <- data.frame(probability.of.ld=logistic_simple$fitted.values,SMOKING=data$SMOKING)
predicted.data
##     probability.of.ld SMOKING
## 1           0.8518519       1
## 2           0.8908046       0
## 3           0.8518519       1
## 4           0.8908046       0
## 5           0.8518519       1
## 6           0.8518519       1
## 7           0.8908046       0
## 8           0.8908046       0
## 9           0.8908046       0
## 10          0.8908046       0
## 11          0.8908046       0
## 12          0.8518519       1
## 13          0.8908046       0
## 14          0.8908046       0
## 15          0.8908046       0
## 16          0.8518519       1
## 17          0.8908046       0
## 18          0.8908046       0
## 19          0.8908046       0
## 20          0.8518519       1
## 21          0.8908046       0
## 22          0.8518519       1
## 23          0.8908046       0
## 24          0.8908046       0
## 25          0.8908046       0
## 26          0.8518519       1
## 27          0.8908046       0
## 28          0.8518519       1
## 29          0.8908046       0
## 30          0.8518519       1
## 31          0.8908046       0
## 32          0.8908046       0
## 33          0.8908046       0
## 34          0.8908046       0
## 35          0.8518519       1
## 36          0.8908046       0
## 37          0.8518519       1
## 38          0.8518519       1
## 39          0.8908046       0
## 40          0.8908046       0
## 41          0.8908046       0
## 42          0.8518519       1
## 43          0.8518519       1
## 44          0.8908046       0
## 45          0.8908046       0
## 46          0.8908046       0
## 47          0.8908046       0
## 48          0.8908046       0
## 49          0.8518519       1
## 50          0.8518519       1
## 51          0.8518519       1
## 52          0.8908046       0
## 53          0.8908046       0
## 54          0.8908046       0
## 55          0.8518519       1
## 56          0.8518519       1
## 57          0.8518519       1
## 58          0.8518519       1
## 59          0.8518519       1
## 60          0.8908046       0
## 61          0.8518519       1
## 62          0.8518519       1
## 63          0.8518519       1
## 64          0.8518519       1
## 65          0.8518519       1
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## 67          0.8518519       1
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## 69          0.8908046       0
## 70          0.8908046       0
## 71          0.8908046       0
## 72          0.8908046       0
## 73          0.8518519       1
## 74          0.8908046       0
## 75          0.8908046       0
## 76          0.8908046       0
## 77          0.8518519       1
## 78          0.8908046       0
## 79          0.8908046       0
## 80          0.8908046       0
## 81          0.8518519       1
## 82          0.8908046       0
## 83          0.8908046       0
## 84          0.8518519       1
## 85          0.8518519       1
## 86          0.8518519       1
## 87          0.8518519       1
## 88          0.8518519       1
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## 90          0.8908046       0
## 91          0.8518519       1
## 92          0.8518519       1
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## 94          0.8518519       1
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## 96          0.8518519       1
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## 98          0.8908046       0
## 99          0.8518519       1
## 100         0.8908046       0
## 101         0.8908046       0
## 102         0.8518519       1
## 103         0.8908046       0
## 104         0.8908046       0
## 105         0.8908046       0
## 106         0.8518519       1
## 107         0.8908046       0
## 108         0.8908046       0
## 109         0.8518519       1
## 110         0.8518519       1
## 111         0.8518519       1
## 112         0.8908046       0
## 113         0.8518519       1
## 114         0.8908046       0
## 115         0.8518519       1
## 116         0.8518519       1
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## 118         0.8908046       0
## 119         0.8908046       0
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## 125         0.8908046       0
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## 308         0.8908046       0
## 309         0.8518519       1
## We can plot the data...

xtabs(~ probability.of.ld + SMOKING, data=predicted.data)
##                    SMOKING
## probability.of.ld     0   1
##   0.851851851851851   0 135
##   0.890804597474673 174   0
# There are 135 individuals predicted to have a probability of 0.851851851851851 of lung cancer who are non-smokers, and there are 174 individuals predicted to have a probability of 0.890804597474673 of lung cancer who are smokers. This output can be used to evaluate the performance of a binary logistic regression model that was used to predict the probability of lung cancer based on smoking status.
logistic <- glm(LUNG_CANCER ~ ., data=data, family="binomial")
## Warning: glm.fit: algorithm did not converge
summary(logistic)
## 
## Call:
## glm(formula = LUNG_CANCER ~ ., family = "binomial", data = data)
## 
## Deviance Residuals: 
##   [1]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
##  [26]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
##  [51]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
##  [76]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [101]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [126]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [151]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [176]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [201]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [226]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [251]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [276]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
## [301]  0  0  0  0  0  0  0  0  0
## 
## Coefficients: (322 not defined because of singularities)
##                          Estimate Std. Error z value Pr(>|z|)
## (Intercept)             7.173e+02  1.736e+07       0        1
## GENDER                 -7.439e+02  8.039e+07       0        1
## AGE                     4.463e-06  5.036e+05       0        1
## SMOKING1                1.435e+03  1.116e+08       0        1
## YELLOW_FINGERS1         1.594e+02  2.346e+07       0        1
## ANXIETY1                4.782e+02  4.028e+07       0        1
## PEER_PRESSURE1         -5.313e+01  1.038e+07       0        1
## CHRONIC_DISEASE1       -1.328e+03  9.016e+07       0        1
## FATIGUE1               -1.222e+03  9.103e+07       0        1
## ALLERGY1                1.169e+03  8.746e+07       0        1
## WHEEZING1               1.063e+02  2.547e+07       0        1
## ALCOHOL_CONSUMING      -4.782e+02  4.406e+07       0        1
## COUGHING1              -1.806e+03  1.502e+08       0        1
## SHORTNESS_OF_BREATH1    1.116e+03  1.017e+08       0        1
## SWALLOWING_DIFFICULTY1 -4.251e+02  4.648e+07       0        1
## CHEST_PAIN1             4.251e+02  2.650e+07       0        1
## WEIGHT92.74955         -2.072e+03  1.527e+08       0        1
## WEIGHT97.90191          2.657e+02  4.518e+07       0        1
## WEIGHT98.64133          5.313e+02  3.255e+07       0        1
## WEIGHT100.627          -1.594e+02  6.430e+06       0        1
## WEIGHT100.9758          1.806e+03  1.467e+08       0        1
## WEIGHT101.4693          6.907e+02  4.725e+07       0        1
## WEIGHT102.0927          3.188e+02  3.566e+07       0        1
## WEIGHT102.8114         -4.782e+02  4.383e+07       0        1
## WEIGHT102.8351          1.488e+03  1.131e+08       0        1
## WEIGHT103.3016         -1.275e+03  9.002e+07       0        1
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## WEIGHT104.8265          3.719e+03  2.862e+08       0        1
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## HEIGHT_INCH69.43393            NA         NA      NA       NA
## HEIGHT_INCH69.43706            NA         NA      NA       NA
## HEIGHT_INCH69.47115            NA         NA      NA       NA
## HEIGHT_INCH69.48146            NA         NA      NA       NA
## HEIGHT_INCH69.51862            NA         NA      NA       NA
## HEIGHT_INCH69.5233             NA         NA      NA       NA
## HEIGHT_INCH69.54011            NA         NA      NA       NA
## HEIGHT_INCH69.57212            NA         NA      NA       NA
## HEIGHT_INCH69.64403            NA         NA      NA       NA
## HEIGHT_INCH69.65814            NA         NA      NA       NA
## HEIGHT_INCH69.66158            NA         NA      NA       NA
## HEIGHT_INCH69.67258            NA         NA      NA       NA
## HEIGHT_INCH69.70745            NA         NA      NA       NA
## HEIGHT_INCH69.71947            NA         NA      NA       NA
## HEIGHT_INCH69.76212            NA         NA      NA       NA
## HEIGHT_INCH69.78765            NA         NA      NA       NA
## HEIGHT_INCH69.80204            NA         NA      NA       NA
## HEIGHT_INCH69.82117            NA         NA      NA       NA
## HEIGHT_INCH69.83048            NA         NA      NA       NA
## HEIGHT_INCH69.89473            NA         NA      NA       NA
## HEIGHT_INCH69.91479            NA         NA      NA       NA
## HEIGHT_INCH69.9236             NA         NA      NA       NA
## HEIGHT_INCH69.92442            NA         NA      NA       NA
## HEIGHT_INCH69.92983            NA         NA      NA       NA
## HEIGHT_INCH69.93715            NA         NA      NA       NA
## HEIGHT_INCH69.98149            NA         NA      NA       NA
## HEIGHT_INCH70.007              NA         NA      NA       NA
## HEIGHT_INCH70.01309            NA         NA      NA       NA
## HEIGHT_INCH70.01472            NA         NA      NA       NA
## HEIGHT_INCH70.05098            NA         NA      NA       NA
## HEIGHT_INCH70.05147            NA         NA      NA       NA
## HEIGHT_INCH70.06306            NA         NA      NA       NA
## HEIGHT_INCH70.09297            NA         NA      NA       NA
## HEIGHT_INCH70.09805            NA         NA      NA       NA
## HEIGHT_INCH70.1459             NA         NA      NA       NA
## HEIGHT_INCH70.16973            NA         NA      NA       NA
## HEIGHT_INCH70.1766             NA         NA      NA       NA
## HEIGHT_INCH70.18447            NA         NA      NA       NA
## HEIGHT_INCH70.18602            NA         NA      NA       NA
## HEIGHT_INCH70.19025            NA         NA      NA       NA
## HEIGHT_INCH70.241              NA         NA      NA       NA
## HEIGHT_INCH70.24256            NA         NA      NA       NA
## HEIGHT_INCH70.26611            NA         NA      NA       NA
## HEIGHT_INCH70.26939            NA         NA      NA       NA
## HEIGHT_INCH70.40617            NA         NA      NA       NA
## HEIGHT_INCH70.55703            NA         NA      NA       NA
## HEIGHT_INCH70.59505            NA         NA      NA       NA
## HEIGHT_INCH70.70844            NA         NA      NA       NA
## HEIGHT_INCH70.7301             NA         NA      NA       NA
## HEIGHT_INCH70.80592            NA         NA      NA       NA
## HEIGHT_INCH70.84235            NA         NA      NA       NA
## HEIGHT_INCH70.84278            NA         NA      NA       NA
## HEIGHT_INCH70.98112            NA         NA      NA       NA
## HEIGHT_INCH71.0916             NA         NA      NA       NA
## HEIGHT_INCH71.09585            NA         NA      NA       NA
## HEIGHT_INCH71.14106            NA         NA      NA       NA
## HEIGHT_INCH71.23033            NA         NA      NA       NA
## HEIGHT_INCH71.23161            NA         NA      NA       NA
## HEIGHT_INCH71.39044            NA         NA      NA       NA
## HEIGHT_INCH71.48752            NA         NA      NA       NA
## HEIGHT_INCH71.51521            NA         NA      NA       NA
## HEIGHT_INCH71.55542            NA         NA      NA       NA
## HEIGHT_INCH71.80484            NA         NA      NA       NA
## HEIGHT_INCH71.82178            NA         NA      NA       NA
## HEIGHT_INCH72.01515            NA         NA      NA       NA
## HEIGHT_INCH72.44434            NA         NA      NA       NA
## HEIGHT_INCH72.74676            NA         NA      NA       NA
## HEIGHT_INCH73.26872            NA         NA      NA       NA
## HEIGHT_INCH73.83364            NA         NA      NA       NA
## HEIGHT_INCH73.90107            NA         NA      NA       NA
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2.3430e+02  on 308  degrees of freedom
## Residual deviance: 1.7927e-09  on   0  degrees of freedom
## AIC: 618
## 
## Number of Fisher Scoring iterations: 25
## Now calculate the overall "Pseudo R-squared" and its p-value
ll.null <- logistic$null.deviance/-2
ll.proposed <- logistic$deviance/-2
(ll.null - ll.proposed) / ll.null
## [1] 1
## The p-value for the R^2
1 - pchisq(2*(ll.proposed - ll.null), df=(length(logistic$coefficients)-1))
## [1] 1
predicted.data <- data.frame(probability.of.ld=logistic$fitted.values,LUNG_CANCER=data$LUNG_CANCER)
predicted.data <- predicted.data[order(predicted.data$probability.of.ld, decreasing=FALSE),]
predicted.data$rank <- 1:nrow(predicted.data)
## Lastly, we can plot the predicted probabilities for each sample having
## heart disease and color by whether or not they actually had heart disease
ggplot(data=predicted.data, aes(x=rank, y=probability.of.ld)) +
geom_point(aes(color=LUNG_CANCER), alpha=1, shape=4, stroke=2) +
xlab("Index") +
ylab("Predicted probability of getting lung cancer")

# From Caret
pdata <- predict(logistic,newdata=data,type="response" )
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
pdata
##            1            2            3            4            5            6 
## 1.000000e+00 1.000000e+00 2.900701e-12 2.900701e-12 2.900701e-12 1.000000e+00 
##            7            8            9           10           11           12 
## 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 
##           13           14           15           16           17           18 
## 2.900701e-12 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 
##           19           20           21           22           23           24 
## 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 
##           25           26           27           28           29           30 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 2.900701e-12 
##           31           32           33           34           35           36 
## 2.900701e-12 1.000000e+00 2.900701e-12 1.000000e+00 2.900701e-12 1.000000e+00 
##           37           38           39           40           41           42 
## 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           43           44           45           46           47           48 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           49           50           51           52           53           54 
## 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           55           56           57           58           59           60 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           61           62           63           64           65           66 
## 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           67           68           69           70           71           72 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           73           74           75           76           77           78 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           79           80           81           82           83           84 
## 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 
##           85           86           87           88           89           90 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           91           92           93           94           95           96 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##           97           98           99          100          101          102 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          103          104          105          106          107          108 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          109          110          111          112          113          114 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          115          116          117          118          119          120 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          121          122          123          124          125          126 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          127          128          129          130          131          132 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 
##          133          134          135          136          137          138 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          139          140          141          142          143          144 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          145          146          147          148          149          150 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          151          152          153          154          155          156 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 2.900701e-12 1.000000e+00 
##          157          158          159          160          161          162 
## 2.900701e-12 2.900701e-12 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 
##          163          164          165          166          167          168 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          169          170          171          172          173          174 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 
##          175          176          177          178          179          180 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          181          182          183          184          185          186 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 
##          187          188          189          190          191          192 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          193          194          195          196          197          198 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          199          200          201          202          203          204 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          205          206          207          208          209          210 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 
##          211          212          213          214          215          216 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 
##          217          218          219          220          221          222 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 
##          223          224          225          226          227          228 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          229          230          231          232          233          234 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          235          236          237          238          239          240 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          241          242          243          244          245          246 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 
##          247          248          249          250          251          252 
## 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 
##          253          254          255          256          257          258 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          259          260          261          262          263          264 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 
##          265          266          267          268          269          270 
## 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 
##          271          272          273          274          275          276 
## 2.900701e-12 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 
##          277          278          279          280          281          282 
## 1.000000e+00 2.900701e-12 1.000000e+00 1.000000e+00 2.900701e-12 2.900701e-12 
##          283          284          285          286          287          288 
## 2.900701e-12 1.000000e+00 1.000000e+00 1.000000e+00 2.900701e-12 1.000000e+00 
##          289          290          291          292          293          294 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          295          296          297          298          299          300 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          301          302          303          304          305          306 
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 
##          307          308          309 
## 1.000000e+00 1.000000e+00 1.000000e+00
data$LUNG_CANCER
##   [1] 1 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1
##  [38] 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
##  [75] 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [149] 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1
## [260] 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 1 1 1 1
pdataF <- as.factor(ifelse(test = as.numeric(pdata > 0.5) == 0, "Healthy", "Unhealthy"))

#From e1071::
#confusionMatrix(pdataF, data$LUNG_CANCER)
# From pROC
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     plot = TRUE)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 1
par(pty = "s")
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     plot = TRUE)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 1
## NOTE: By default, roc() uses specificity on the x-axis and the values range
## from 1 to 0. This makes the graph look like what we would expect, but the
## x-axis itself might induce a headache. To use 1-specificity (i.e. the
## False Positive Rate) on the x-axis, set "legacy.axes" to TRUE.
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 1
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage")
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage")
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 1
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 1
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 1
## If we want to find out the optimal threshold we can store the
## data used to make the ROC graph in a variable...
roc.info <- roc(data$LUNG_CANCER, logistic$fitted.values, legacy.axes=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
str(roc.info)
## List of 15
##  $ percent           : logi FALSE
##  $ sensitivities     : num [1:37] 1 1 1 1 1 1 1 1 1 1 ...
##  $ specificities     : num [1:37] 0 0.0256 0.0513 0.0769 0.1026 ...
##  $ thresholds        : num [1:37] -Inf 2.9e-12 2.9e-12 2.9e-12 2.9e-12 ...
##  $ direction         : chr "<"
##  $ cases             : Named num [1:270] 1 1 1 1 1 ...
##   ..- attr(*, "names")= chr [1:270] "1" "2" "6" "7" ...
##  $ controls          : Named num [1:39] 2.9e-12 2.9e-12 2.9e-12 2.9e-12 2.9e-12 ...
##   ..- attr(*, "names")= chr [1:39] "3" "4" "5" "9" ...
##  $ fun.sesp          :function (thresholds, controls, cases, direction)  
##  $ auc               : 'auc' num 1
##   ..- attr(*, "partial.auc")= logi FALSE
##   ..- attr(*, "percent")= logi FALSE
##   ..- attr(*, "roc")=List of 15
##   .. ..$ percent           : logi FALSE
##   .. ..$ sensitivities     : num [1:37] 1 1 1 1 1 1 1 1 1 1 ...
##   .. ..$ specificities     : num [1:37] 0 0.0256 0.0513 0.0769 0.1026 ...
##   .. ..$ thresholds        : num [1:37] -Inf 2.9e-12 2.9e-12 2.9e-12 2.9e-12 ...
##   .. ..$ direction         : chr "<"
##   .. ..$ cases             : Named num [1:270] 1 1 1 1 1 ...
##   .. .. ..- attr(*, "names")= chr [1:270] "1" "2" "6" "7" ...
##   .. ..$ controls          : Named num [1:39] 2.9e-12 2.9e-12 2.9e-12 2.9e-12 2.9e-12 ...
##   .. .. ..- attr(*, "names")= chr [1:39] "3" "4" "5" "9" ...
##   .. ..$ fun.sesp          :function (thresholds, controls, cases, direction)  
##   .. ..$ auc               : 'auc' num 1
##   .. .. ..- attr(*, "partial.auc")= logi FALSE
##   .. .. ..- attr(*, "percent")= logi FALSE
##   .. .. ..- attr(*, "roc")=List of 8
##   .. .. .. ..$ percent      : logi FALSE
##   .. .. .. ..$ sensitivities: num [1:37] 1 1 1 1 1 1 1 1 1 1 ...
##   .. .. .. ..$ specificities: num [1:37] 0 0.0256 0.0513 0.0769 0.1026 ...
##   .. .. .. ..$ thresholds   : num [1:37] -Inf 2.9e-12 2.9e-12 2.9e-12 2.9e-12 ...
##   .. .. .. ..$ direction    : chr "<"
##   .. .. .. ..$ cases        : Named num [1:270] 1 1 1 1 1 ...
##   .. .. .. .. ..- attr(*, "names")= chr [1:270] "1" "2" "6" "7" ...
##   .. .. .. ..$ controls     : Named num [1:39] 2.9e-12 2.9e-12 2.9e-12 2.9e-12 2.9e-12 ...
##   .. .. .. .. ..- attr(*, "names")= chr [1:39] "3" "4" "5" "9" ...
##   .. .. .. ..$ fun.sesp     :function (thresholds, controls, cases, direction)  
##   .. .. .. ..- attr(*, "class")= chr "roc"
##   .. ..$ call              : language roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,      legacy.axes = TRUE)
##   .. ..$ original.predictor: Named num [1:309] 1.0 1.0 2.9e-12 2.9e-12 2.9e-12 ...
##   .. .. ..- attr(*, "names")= chr [1:309] "1" "2" "3" "4" ...
##   .. ..$ original.response : num [1:309] 1 1 0 0 0 1 1 1 0 1 ...
##   .. ..$ predictor         : Named num [1:309] 1.0 1.0 2.9e-12 2.9e-12 2.9e-12 ...
##   .. .. ..- attr(*, "names")= chr [1:309] "1" "2" "3" "4" ...
##   .. ..$ response          : num [1:309] 1 1 0 0 0 1 1 1 0 1 ...
##   .. ..$ levels            : chr [1:2] "0" "1"
##   .. ..- attr(*, "class")= chr "roc"
##  $ call              : language roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,      legacy.axes = TRUE)
##  $ original.predictor: Named num [1:309] 1.0 1.0 2.9e-12 2.9e-12 2.9e-12 ...
##   ..- attr(*, "names")= chr [1:309] "1" "2" "3" "4" ...
##  $ original.response : num [1:309] 1 1 0 0 0 1 1 1 0 1 ...
##  $ predictor         : Named num [1:309] 1.0 1.0 2.9e-12 2.9e-12 2.9e-12 ...
##   ..- attr(*, "names")= chr [1:309] "1" "2" "3" "4" ...
##  $ response          : num [1:309] 1 1 0 0 0 1 1 1 0 1 ...
##  $ levels            : chr [1:2] "0" "1"
##  - attr(*, "class")= chr "roc"
## tpp = true positive percentage
## fpp = false positive precentage
roc.df <- data.frame(tpp=roc.info$sensitivities*100, fpp=(1 - roc.info$specificities)*100,thresholds=roc.info$thresholds)
roc.df
##    tpp        fpp   thresholds
## 1  100 100.000000         -Inf
## 2  100  97.435897 2.900701e-12
## 3  100  94.871795 2.900701e-12
## 4  100  92.307692 2.900701e-12
## 5  100  89.743590 2.900701e-12
## 6  100  87.179487 2.900701e-12
## 7  100  84.615385 2.900701e-12
## 8  100  82.051282 2.900701e-12
## 9  100  79.487179 2.900701e-12
## 10 100  76.923077 2.900701e-12
## 11 100  74.358974 2.900701e-12
## 12 100  71.794872 2.900701e-12
## 13 100  69.230769 2.900701e-12
## 14 100  66.666667 2.900701e-12
## 15 100  64.102564 2.900701e-12
## 16 100  61.538462 2.900701e-12
## 17 100  58.974359 2.900701e-12
## 18 100  56.410256 2.900701e-12
## 19 100  53.846154 2.900701e-12
## 20 100  48.717949 2.900701e-12
## 21 100  46.153846 2.900701e-12
## 22 100  41.025641 2.900701e-12
## 23 100  38.461538 2.900701e-12
## 24 100  35.897436 2.900701e-12
## 25 100  33.333333 2.900701e-12
## 26 100  30.769231 2.900701e-12
## 27 100  28.205128 2.900701e-12
## 28 100  23.076923 2.900701e-12
## 29 100  20.512821 2.900701e-12
## 30 100  17.948718 2.900701e-12
## 31 100  12.820513 2.900701e-12
## 32 100  10.256410 2.900701e-12
## 33 100   7.692308 2.900701e-12
## 34 100   5.128205 2.900701e-12
## 35 100   2.564103 2.900701e-12
## 36 100   0.000000 5.000000e-01
## 37   0   0.000000          Inf
head(roc.df) 
##   tpp       fpp   thresholds
## 1 100 100.00000         -Inf
## 2 100  97.43590 2.900701e-12
## 3 100  94.87179 2.900701e-12
## 4 100  92.30769 2.900701e-12
## 5 100  89.74359 2.900701e-12
## 6 100  87.17949 2.900701e-12
## head() will show us the values for the upper right-hand corner of the ROC graph, when the threshold is so low
## (negative infinity) that every single sample is called "obese".
## Thus TPP = 100% and FPP = 100%
tail(roc.df) 
##    tpp       fpp   thresholds
## 32 100 10.256410 2.900701e-12
## 33 100  7.692308 2.900701e-12
## 34 100  5.128205 2.900701e-12
## 35 100  2.564103 2.900701e-12
## 36 100  0.000000 5.000000e-01
## 37   0  0.000000          Inf
## tail() will show us the values for the lower left-hand corner
## of the ROC graph, when the threshold is so high (infinity)
## that every single sample is called "not obese".
## Thus, TPP = 0% and FPP = 0%
## now let's look at the thresholds between TPP 60% and 80%
roc.df[roc.df$tpp > 60 & roc.df$tpp < 80,]
## [1] tpp        fpp        thresholds
## <0 rows> (or 0-length row.names)
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 100%
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 100%
roc(data$LUNG_CANCER,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE, partial.auc=c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x=45)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases

## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE, partial.auc = c(100, 90), auc.polygon = TRUE,     auc.polygon.col = "#377eb822", print.auc.x = 45)
## 
## Data: logistic$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Partial area under the curve (specificity 100%-90%): 10%
# Lets do two roc plots to understand which model is better
roc(data$LUNG_CANCER, logistic_simple$fitted.values, plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, print.auc=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
## 
## Call:
## roc.default(response = data$LUNG_CANCER, predictor = logistic_simple$fitted.values,     percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage",     ylab = "True Postive Percentage", col = "#377eb8", lwd = 4,     print.auc = TRUE)
## 
## Data: logistic_simple$fitted.values in 39 controls (data$LUNG_CANCER 0) < 270 cases (data$LUNG_CANCER 1).
## Area under the curve: 54.34%
# Lets add the other graph
plot.roc(data$LUNG_CANCER, logistic$fitted.values, percent=TRUE, col="#4daf4a", lwd=4, print.auc=TRUE, add=TRUE, print.auc.y=40)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
legend("bottomright", legend=c("Simple", "Non Simple"), col=c("#377eb8", "#4daf4a"), lwd=4) 

# The simple line on the graph is generated when the model is a random classifier, which means that it predicts classes at random. The non-simple line on the graph is generated when the model is a non-random classifier, which means that it makes informed predictions based on the features of the data.The TPP is the percentage of actual positive instances that the model correctly identifies as positive, while the FPP is the percentage of actual negative instances that the model incorrectly identifies as positive. An AUC of 100% for the non-simple line indicates that it has correctly classified all the samples in the dataset, while an AUC of 54.3% for the simple line indicates that it has not performed much better than randomly assigning class labels. This suggests that the non-simple line is a more reliable classifier than the simple line for this particular dataset. This means that the non-simple model captures more of the variation in the data and provides better discrimination between the two classes. Therefore, the goal to accurately classify data, the non-simple model would be preferred over the simple model.
library(readr)
library(MVA)
## Loading required package: HSAUR2
## Loading required package: tools
## 
## Attaching package: 'HSAUR2'
## 
## The following object is masked from 'package:tidyr':
## 
##     household
library(HSAUR2)
library(SciViews)
library(scatterplot3d)
library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:psych':
## 
##     logit
## 
## The following object is masked from 'package:purrr':
## 
##     some
## 
## The following object is masked from 'package:dplyr':
## 
##     recode
library(lattice)
library(GGally)
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(ggplot2)
library(ggridges)
library(ggvis)
library(ggthemes)
library(cowplot)
library(gapminder)
library(gganimate)
library(dplyr)
library(tidyverse)
library(grid)
library(gridExtra)
library(RColorBrewer)
library(Hotelling)
## Loading required package: corpcor
## 
## Attaching package: 'Hotelling'
## 
## The following object is masked from 'package:dplyr':
## 
##     summarise
library(stats)
library(biotools)
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## 
## The following object is masked from 'package:dplyr':
## 
##     select
## 
## ---
## biotools version 4.2
library(factoextra)
library(FactoMineR)
library(ggfortify)
library(psych)
library(corrplot)
library(stringr)
library(ellipse)
## 
## Attaching package: 'ellipse'
## 
## The following object is masked from 'package:car':
## 
##     ellipse
## 
## The following object is masked from 'package:graphics':
## 
##     pairs
library(ggplot2)
library(reshape2)
## 
## Attaching package: 'reshape2'
## 
## The following object is masked from 'package:tidyr':
## 
##     smiths
library(caret)
## 
## Attaching package: 'caret'
## 
## The following object is masked from 'package:purrr':
## 
##     lift
library(pROC)
library(cluster)
library(factoextra)
library(psych)

EFA

# Factor Analysis

library(psych)
library(readr)
data <- read_csv("/Users/batul/Desktop/MVA/LUNGCANCER3.csv")
## Rows: 309 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (18): LUNG_CANCER, GENDER, AGE, SMOKING, YELLOW_FINGERS, ANXIETY, PEER_P...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
attach(data)
## The following objects are masked from cancer (pos = 28):
## 
##     AGE, ALCOHOL_CONSUMING, ALLERGY, ANXIETY, CHEST_PAIN,
##     CHRONIC_DISEASE, COUGHING, FATIGUE, GENDER, HEIGHT_INCH,
##     LUNG_CANCER, PEER_PRESSURE, SHORTNESS_OF_BREATH, SMOKING,
##     SWALLOWING_DIFFICULTY, WEIGHT, WHEEZING, YELLOW_FINGERS
## 
## The following objects are masked from cancer (pos = 48):
## 
##     AGE, ALCOHOL_CONSUMING, ALLERGY, ANXIETY, CHEST_PAIN,
##     CHRONIC_DISEASE, COUGHING, FATIGUE, GENDER, HEIGHT_INCH,
##     LUNG_CANCER, PEER_PRESSURE, SHORTNESS_OF_BREATH, SMOKING,
##     SWALLOWING_DIFFICULTY, WEIGHT, WHEEZING, YELLOW_FINGERS
data[1]
## # A tibble: 309 × 1
##    LUNG_CANCER
##          <dbl>
##  1           1
##  2           1
##  3           0
##  4           0
##  5           0
##  6           1
##  7           1
##  8           1
##  9           0
## 10           1
## # … with 299 more rows
fit.pc <- principal(data[-1], nfactors=7, rotate="varimax")
fit.pc
## Principal Components Analysis
## Call: principal(r = data[-1], nfactors = 7, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                         RC1   RC5   RC2   RC3   RC4   RC6   RC7   h2   u2 com
## GENDER                 0.24 -0.61  0.21  0.00 -0.02  0.39 -0.08 0.63 0.37 2.4
## AGE                    0.06 -0.03 -0.03 -0.04  0.10  0.03  0.81 0.68 0.32 1.1
## SMOKING               -0.15 -0.30 -0.23  0.22  0.61  0.16  0.15 0.63 0.37 2.7
## YELLOW_FINGERS         0.74 -0.20 -0.01  0.08 -0.07 -0.03  0.18 0.63 0.37 1.3
## ANXIETY                0.75 -0.08 -0.12 -0.03 -0.35 -0.07  0.18 0.75 0.25 1.7
## PEER_PRESSURE          0.59 -0.24 -0.05  0.04  0.29  0.08 -0.29 0.59 0.41 2.5
## CHRONIC_DISEASE        0.02 -0.04 -0.08  0.04 -0.05  0.89  0.00 0.80 0.20 1.0
## FATIGUE               -0.07 -0.11  0.75  0.03  0.23 -0.06 -0.17 0.66 0.34 1.4
## ALLERGY               -0.09  0.57  0.06  0.04  0.16  0.42  0.07 0.55 0.45 2.2
## WHEEZING               0.04  0.32  0.16 -0.04  0.68 -0.07  0.01 0.60 0.40 1.6
## ALCOHOL_CONSUMING     -0.18  0.67 -0.33 -0.07  0.28  0.02  0.07 0.68 0.32 2.1
## COUGHING              -0.08  0.21  0.35 -0.04  0.52 -0.18  0.42 0.65 0.35 3.5
## SHORTNESS_OF_BREATH   -0.17 -0.01  0.82  0.00 -0.10  0.02  0.15 0.74 0.26 1.2
## SWALLOWING_DIFFICULTY  0.77  0.13 -0.12  0.03  0.05  0.06 -0.12 0.66 0.34 1.2
## CHEST_PAIN             0.03  0.74  0.09  0.12 -0.06 -0.03 -0.09 0.59 0.41 1.1
## WEIGHT                -0.02  0.03 -0.02  0.86  0.06  0.04  0.00 0.74 0.26 1.0
## HEIGHT_INCH            0.11  0.06  0.04  0.84 -0.01  0.01 -0.06 0.73 0.27 1.1
## 
##                        RC1  RC5  RC2  RC3  RC4  RC6  RC7
## SS loadings           2.24 2.08 1.65 1.54 1.50 1.20 1.10
## Proportion Var        0.13 0.12 0.10 0.09 0.09 0.07 0.06
## Cumulative Var        0.13 0.25 0.35 0.44 0.53 0.60 0.67
## Proportion Explained  0.20 0.18 0.15 0.14 0.13 0.11 0.10
## Cumulative Proportion 0.20 0.38 0.53 0.66 0.80 0.90 1.00
## 
## Mean item complexity =  1.7
## Test of the hypothesis that 7 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.08 
##  with the empirical chi square  502.71  with prob <  1.9e-82 
## 
## Fit based upon off diagonal values = 0.78
round(fit.pc$values, 3)
##  [1] 2.865 1.958 1.689 1.473 1.304 1.072 0.954 0.891 0.816 0.714 0.633 0.586
## [13] 0.531 0.516 0.404 0.319 0.277
fit.pc$loadings
## 
## Loadings:
##                       RC1    RC5    RC2    RC3    RC4    RC6    RC7   
## GENDER                 0.238 -0.608  0.209                0.391       
## AGE                                                              0.812
## SMOKING               -0.146 -0.300 -0.229  0.223  0.605  0.163  0.154
## YELLOW_FINGERS         0.739 -0.202                              0.182
## ANXIETY                0.752        -0.124        -0.349         0.180
## PEER_PRESSURE          0.594 -0.241                0.293        -0.289
## CHRONIC_DISEASE                                           0.886       
## FATIGUE                      -0.111  0.747         0.231        -0.167
## ALLERGY                       0.568                0.162  0.421       
## WHEEZING                      0.325  0.155         0.681              
## ALCOHOL_CONSUMING     -0.178  0.674 -0.333         0.276              
## COUGHING                      0.212  0.354         0.517 -0.178  0.421
## SHORTNESS_OF_BREATH   -0.174         0.823        -0.104         0.147
## SWALLOWING_DIFFICULTY  0.775  0.135 -0.122                      -0.123
## CHEST_PAIN                    0.744         0.117                     
## WEIGHT                                      0.857                     
## HEIGHT_INCH            0.105                0.845                     
## 
##                  RC1   RC5   RC2   RC3   RC4   RC6   RC7
## SS loadings    2.242 2.084 1.646 1.536 1.499 1.204 1.104
## Proportion Var 0.132 0.123 0.097 0.090 0.088 0.071 0.065
## Cumulative Var 0.132 0.254 0.351 0.442 0.530 0.601 0.665
#The loadings table shows how strongly each item is associated with each factor, with larger absolute values indicating stronger associations. For example, in the first row we see that GENDER has a loading of 0.238 on the first factor (RC1), -0.608 on the fifth factor (RC5), 0.209 on the second factor (RC2), and no significant loading on the other factors.
# Loadings with more digits
for (i in c(1,3,2,4,5,6,7)) { print(fit.pc$loadings[[1,i]])}
## [1] 0.2376566
## [1] 0.2091599
## [1] -0.6082549
## [1] 0.003326137
## [1] -0.0188464
## [1] 0.3913377
## [1] -0.08192975
# Communalities
fit.pc$communality
##                GENDER                   AGE               SMOKING 
##             0.6304266             0.6770701             0.6301106 
##        YELLOW_FINGERS               ANXIETY         PEER_PRESSURE 
##             0.6318961             0.7475012             0.5911141 
##       CHRONIC_DISEASE               FATIGUE               ALLERGY 
##             0.7978935             0.6613568             0.5453794 
##              WHEEZING     ALCOHOL_CONSUMING              COUGHING 
##             0.6020532             0.6845913             0.6534088 
##   SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY            CHEST_PAIN 
##             0.7407695             0.6556043             0.5893593 
##                WEIGHT           HEIGHT_INCH 
##             0.7410355             0.7335716
# The variable GENDER, the communality estimate is 0.6304266. This means that 63.04% of the variance in GENDER is accounted for by the factors in the analysis. Similarly, for AGE, the communality estimate is 0.6770701, which means that 67.71% of the variance in AGE is accounted for by the factors.
# Rotated factor scores, Notice the columns ordering: RC1, RC3, RC2 and RC4
fit.pc$scores
##                 RC1          RC5          RC2          RC3          RC4
##   [1,]  0.826480088  0.565288896  0.382211396 -1.097397929  0.760114393
##   [2,] -0.549203489  0.878516107  0.845029758  1.624653230 -1.759320426
##   [3,] -0.698405881 -0.954365204  0.945158199  1.807157994  1.339240947
##   [4,]  0.569246677  0.773899168 -1.710458875  0.932681327 -1.705658351
##   [5,] -0.813187090 -1.642216651 -0.154539167  0.988227696  0.670947701
##   [6,] -0.579547502 -1.045911837  1.009371909  0.167537245  0.869382981
##   [7,] -1.194476961  0.862083475  0.797119270  1.156785815  0.039347941
##   [8,]  1.197108273 -0.558413157  0.998567769  0.984445317 -1.018584635
##   [9,] -0.694356054 -1.464451134 -0.423394012 -0.665161430 -1.419213915
##  [10,]  1.178420284  1.333406886 -1.469774951 -0.703154701 -1.053343308
##  [11,]  1.466382712 -0.870646311  1.271411329 -0.692483170  0.406865857
##  [12,] -1.223643169  0.916222000  0.495950311 -0.585976294  0.899804501
##  [13,] -1.464666935 -1.439466386  0.669767021  0.124092395 -1.341876607
##  [14,] -1.072671043  1.410493049  0.951314639 -0.536067875  0.173863236
##  [15,] -1.035284954  1.345544995 -1.091665064 -0.500485112  0.146965626
##  [16,]  1.272491665 -0.630244127  1.119980466  1.425587081  1.217512939
##  [17,] -1.143500984  1.462455556 -0.060874933 -0.419283323 -0.310496714
##  [18,]  1.071079090  0.718904323 -1.681050123  0.922302557 -1.201066590
##  [19,]  0.507873198 -1.346982328  1.142629500  1.401843770 -0.881911563
##  [20,] -1.705697205 -1.904435788  0.224489558 -0.110244516 -0.535311917
##  [21,]  1.043960706 -1.103904164  0.812824448  0.533267247 -1.099300808
##  [22,]  1.280807056 -0.868193003 -1.036979697  1.028266080  1.383061646
##  [23,] -1.521834073 -0.624015438  0.995762194 -2.726338999 -1.105371370
##  [24,] -1.077435816  1.421107276  0.953752826  0.176111551  0.114757908
##  [25,]  1.501475396  1.578901380 -1.040627352  0.359791932  0.315524862
##  [26,]  0.765467482  0.602518396  0.393260527  0.098315351  0.698925206
##  [27,]  0.818107205  0.982050012  0.837881451  1.613955405 -1.683416391
##  [28,] -0.733578790 -0.523846082  0.635453682  0.323466020  1.313253260
##  [29,]  0.937301587  0.718956126 -0.109574502 -1.433412914 -1.009980075
##  [30,] -0.864112699 -0.625267503  0.165587873 -1.211826811  1.324024020
##  [31,] -0.777213569 -1.373572160 -0.110234884 -0.488859165 -1.677160675
##  [32,]  0.199041922  1.749496311 -0.382522858 -1.014112391 -0.934409342
##  [33,]  0.422732862 -0.488401152 -0.430555170  0.052161761 -2.012838608
##  [34,]  0.753706138 -0.087096224  0.099447272  1.360723788 -2.436074493
##  [35,]  0.443224470 -0.230766760 -1.685248187  2.225809213 -1.181434478
##  [36,]  0.540476294 -0.901992256 -0.125761859  0.465401804 -2.102881397
##  [37,] -0.785399535 -0.227630976 -0.164198065  0.711035057  0.248801337
##  [38,] -0.781307686 -1.273507679 -0.526235156 -0.303787301  0.259395705
##  [39,] -1.311636841  0.281033497 -0.136614257  0.231816901 -1.175863170
##  [40,] -1.106274378  1.396970611 -1.090371929 -2.245068993  0.198381435
##  [41,] -0.588487246  1.283216625  0.788296838  0.118398919 -1.267429824
##  [42,] -0.240487061 -0.093165944 -1.259898874 -0.994787083  1.935475600
##  [43,]  0.412247057 -1.359132786 -1.062846264  1.021376290  1.013706495
##  [44,] -0.692281935  1.166010738  0.571421412  0.363998882  0.196750957
##  [45,]  0.592710001 -0.723581368 -1.318672755 -1.769325984  0.247781969
##  [46,]  1.541311527  1.023315054  0.839872551  0.086193129  0.238204214
##  [47,]  0.024187264  0.972623846  0.319280935  0.745993779 -1.378181277
##  [48,]  1.071736963  0.238737571  0.037479496 -0.770791836  1.308985736
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##  [82,]  1.140407208 -1.162293439  0.789686141 -0.670473209 -1.064016094
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##  [84,] -1.076383694 -0.824328853 -0.675341345 -0.373920747  0.609871851
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##  [94,]  1.273410960 -0.061538249 -0.246999189 -0.528475991  1.255925889
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##  [99,]  1.030822370 -0.691831569 -0.527393754 -0.099102179  0.769538330
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## [102,]  1.579503912 -0.029088895  1.188955864 -0.006858820  0.999442364
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## [105,]  1.567285043 -0.368052937  1.342889173 -0.563783564 -0.699171392
## [106,] -1.697405657 -1.882736973  0.244057706  0.119172024 -0.558213327
## [107,]  1.170762184 -1.181079072  0.775841650 -0.352646414 -1.115400298
## [108,]  1.531529801  1.009050805 -1.085874574 -0.778616931 -0.053169977
## [109,] -1.153857491 -0.608107981 -0.500290494  0.467149785  0.617500551
## [110,] -1.706799702  0.598130764 -0.039387787 -0.881947063 -0.442028034
## [111,]  0.774755487  0.650537711  0.441205194 -0.125360549  0.719801993
## [112,]  0.734651661  1.478861605  0.573597501  0.751625073 -1.723343377
## [113,] -0.577837122 -0.972747149  0.959805714  1.037837514  1.325407979
## [114,]  0.647117660  0.762701261 -1.686168570 -1.164392436 -1.571100503
## [115,] -0.653556279 -1.132267884  0.439441370  0.449948788  1.206396661
## [116,] -0.610802330 -1.035534224  1.010553481  0.386193640  0.872064472
## [117,] -1.154682537  0.823738102  0.776264594  0.460837420  0.069685201
## [118,]  1.195816991 -0.562881051  0.995019279  0.892669813 -1.010154448
## [119,]  1.500231340 -0.929860626  1.277836447 -1.477682190  0.605679796
## [120,]  1.097998845  0.243844421 -1.667180328  0.901080525 -0.045073581
## [121,]  1.441379569 -0.535081227  0.913903181 -1.093216160  0.422803600
## [122,] -1.237521974  0.950730287  0.528074354 -0.958031956  0.947396362
## [123,] -0.965807797 -0.699786233  0.447648911  0.537712127 -2.019380544
## [124,]  0.170347057  0.209947494  1.087162081  0.393677251 -0.181040537
## [125,] -1.225925619  1.113791840 -1.237871859 -0.873393505 -0.756963284
## [126,]  0.295787236 -1.271484172  0.873766931 -0.712681959  0.296055826
## [127,] -1.115115836  0.822684406  0.799115390 -1.309042627  0.201847260
## [128,]  1.155001779  0.713145452 -1.657396160 -0.401731510 -1.139007629
## [129,]  1.236766529 -1.124150770  1.127312078  0.827293906 -0.484375489
## [130,] -1.701413608 -1.861929051  0.252198451  1.259785592 -0.654726764
## [131,]  1.133403972 -1.206351594  0.785850175  0.323891606 -0.995321614
## [132,]  1.343904904 -0.803058121 -0.964914238  1.097047071  1.344482828
## [133,] -1.383165095 -0.726119520  0.908149879 -0.213229160 -1.437576280
## [134,] -1.043340024  1.270853782  0.835386503 -1.232458711  0.196418343
## [135,]  1.039112517  1.828121696 -0.934451412  0.802813410 -0.385302189
## [136,] -0.101958081 -0.180105743  0.041518159  0.483849350  0.930824542
## [137,]  0.121254548  0.058109212  1.199117795 -0.845208144 -1.922992713
## [138,] -0.723715438 -0.512570025  0.649972794  0.080870364  1.330084730
## [139,]  0.861306432  0.827719745 -0.062299294  2.728011360 -1.316541767
## [140,] -0.847185219 -0.589254761  0.183426367  0.890155726  1.129672810
## [141,]  0.039828638 -0.552789037  1.532858158  0.640291404  0.639270757
## [142,] -0.440334540  0.863584028  0.734945763 -1.518152558 -0.233958670
## [143,]  1.136501663 -0.154928005  0.654726413 -0.034507309 -1.073265156
## [144,]  1.749612814  0.603810283  1.729371540 -0.046596199  0.129466516
## [145,]  1.067431191  0.656407948 -1.984469156 -1.477441705  0.003446725
## [146,]  1.568444972 -0.932263374  1.282040054 -0.626966371  0.483784012
## [147,] -0.689411923  0.972500360  0.656701256  0.663192394  0.866986234
## [148,] -0.341721460 -1.115529080  0.185425946 -1.732657814  1.224506997
## [149,] -1.043250861  1.376592276  0.918514618  0.333080503  0.071491717
## [150,] -1.148658276  1.399531442 -1.075854940  0.683409694  0.124061278
## [151,] -0.585323484  1.305468330  0.806459503  0.445000342 -1.295553071
## [152,] -0.270430494 -0.054395384 -1.241831722  0.286019769  1.846247395
## [153,]  0.436846069 -1.393358234 -1.073107368 -0.792027137  1.154873703
## [154,] -0.935119438 -0.406310893 -1.510717337  0.252547299 -1.014526559
## [155,] -0.291662487 -1.570378573 -1.227546631  1.755832367 -1.004963467
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## [157,] -0.932179665 -0.016673423 -1.233762767  2.643703333 -1.912320748
## [158,] -0.042238635 -0.860855001 -1.014062218 -0.804856612 -0.908300692
## [159,]  0.690007741  0.697890669  0.490356538  1.623487220  0.661652585
## [160,] -0.677058748 -0.979647878 -2.534758759 -1.204439700 -0.077911953
## [161,] -0.799894244  0.080596849 -0.702651085  0.611900555  1.405631915
## [162,]  0.021439235 -0.018875613  0.815771825 -1.885521307 -0.919009868
## [163,]  0.425991486  0.885389090  0.086007832  0.670209182  1.261080448
## [164,]  0.279105604  1.592613041  0.950898516 -0.497193360  0.782191067
## [165,] -0.330742620 -1.043978915 -0.706597515 -0.661840317  1.282616142
## [166,]  0.562762602  0.442338902 -1.660189376 -0.281434759  0.909186152
## [167,] -0.113972062 -1.242388592  0.929827001 -0.028642762  0.469121288
## [168,] -0.837662531  1.079278459 -0.593621565 -0.369546076 -0.113176492
## [169,]  0.507715609 -0.187919099  0.494540841 -0.021204551  0.860222002
## [170,]  0.609454531  1.074391001  0.889061521 -1.276446519 -0.538257047
## [171,]  0.724913075  0.999069882 -0.415599432  0.203657847  1.994863198
## [172,] -0.285749279 -1.809285276 -1.325506299  0.183853183 -0.294606011
## [173,] -0.235763764 -0.254697870 -0.733229631 -0.181350426  2.236240021
## [174,] -0.049732403 -0.176078273 -1.893738410 -1.266730740  0.520729007
## [175,] -0.001534355  0.710387890  0.611931051  2.447379104  1.376121583
## [176,]  1.776831750 -0.116921383  0.482894748 -1.570358302  0.538615892
## [177,] -0.418996647 -0.222105247  1.243568723 -0.242822716  0.689484966
## [178,] -1.309358959 -0.092801375  0.476557048 -1.197011605  0.417489304
## [179,]  1.441540972  0.158103807  1.163187082 -0.742038798 -1.151912302
## [180,]  1.564545492 -0.999263239  1.222814167 -0.969681250  0.507313970
## [181,]  1.191424599  1.202114942 -1.548305206  0.150933393 -0.998091093
## [182,]  1.575147896 -1.020640732  1.208430347 -1.314168671  0.528022931
## [183,] -1.217944273  0.908162159  0.493979469 -1.065357391  0.937800777
## [184,] -1.442710880 -1.404203393  0.659682994  0.133153001 -1.511703515
## [185,] -1.102283714  1.315236390  0.852117322  0.110161838  0.121733649
## [186,] -1.278288103  0.423819393 -1.427411617 -0.671966434  0.419493364
## [187,]  0.252411167 -2.145835682 -0.801154159  0.431433100 -0.122101554
## [188,] -1.581550323 -1.047007036 -0.691909814 -0.562797987 -1.010989473
## [189,]  0.219960073 -1.046968637 -1.577424240 -0.217799790 -1.348991645
## [190,]  0.565071342 -1.677416027 -0.321976922 -1.143898606 -0.813580727
## [191,] -1.689319410 -2.004806216 -0.873953873  1.742822745 -0.347334020
## [192,]  0.431460528 -1.590168640 -0.312801731 -1.518667991 -0.838091937
## [193,]  0.285995268 -1.475343909 -1.248947801  0.084999344 -1.237372586
## [194,] -1.265452250 -2.134387753 -1.872361501  0.921594818  0.061452802
## [195,] -1.575579219  0.756166708  0.359487071  1.633289135 -0.118808164
## [196,]  0.529303317 -0.200227213 -0.822618724 -0.836851816  0.683744666
## [197,] -0.233993222  0.839235834 -0.496930377 -0.736788953 -0.740923897
## [198,]  0.743707167 -0.135953679 -0.625768171  0.464740121  0.189734623
## [199,] -0.149055287 -0.207655786 -1.495484012 -0.037430809 -1.623456545
## [200,]  0.298391478  0.988843749 -0.141517372  0.683268233  0.587457286
## [201,] -0.024328298 -0.299144890 -1.861597323 -0.887821455  1.414487697
## [202,] -1.318405523 -0.347297959  1.040785935 -0.795257655 -0.137787564
## [203,] -0.353683131  1.542527361 -0.502661505  0.805459761 -0.159288593
## [204,]  1.236167206 -0.094681311 -0.292751504  0.340832630  1.197933809
## [205,] -0.468749173  1.488072304  0.775251519  0.052580251 -0.820333080
## [206,]  1.035201940 -0.552905023 -0.828490195  1.126800318 -0.149607593
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## [208,] -1.069552769 -0.944425097 -0.238441611  1.068151630 -0.613446193
## [209,]  1.027667470 -0.655013847 -0.507854288  1.431629962  0.639834524
## [210,] -1.159430869  1.489763469  0.980902989  2.321873875 -0.013043857
## [211,] -1.351112727  0.580490961 -1.306697680  0.242638474  0.408759820
## [212,]  1.562013769 -0.016289911  1.198248016 -0.134041425  1.024324058
## [213,] -1.016857307  1.411072219  0.971187147 -1.427421778  0.216746168
## [214,]  1.203597874  0.687632003 -1.667912453 -0.733260850 -1.145301339
## [215,]  1.459915550 -0.304204026  1.367632355  0.771510516 -0.738192522
## [216,] -1.727189180 -1.910182809  0.211377280  0.277109685 -0.556584241
## [217,]  1.182325126 -1.179592704  0.771127709  0.598215298 -1.208071248
## [218,]  1.558160745  1.057603183 -1.036399296 -0.719829394 -0.069047511
## [219,] -1.040659084 -0.712709073 -0.567554914 -0.155955657  0.582887265
## [220,] -1.542888013  0.694087381  0.316437916  0.820791632 -0.076769724
## [221,]  0.734266676  0.593990104  0.432122547 -1.533073229  0.899959267
## [222,] -0.750101700 -0.944196668 -2.524250348 -0.408843818 -0.095514479
## [223,] -0.642376903  0.052533252 -0.703013559  1.384141268  1.227703615
## [224,]  0.048375496  0.037854139  0.862875127 -0.707816247 -1.034163860
## [225,]  0.429230918  0.872581005  0.096183871 -1.724137159  1.471618069
## [226,]  0.232450398  1.657360946  0.994186094  0.242286600  0.756360867
## [227,] -0.274197249 -0.930469385 -0.600015682  0.366892022  1.169423548
## [228,]  0.614702995  0.388974398 -1.692110258 -1.002981366  0.931558639
## [229,] -0.175980940 -1.220337828  0.931633435  0.616738680  0.455695520
## [230,] -0.800220362  1.157615001 -0.518092789  0.081771169 -0.167066628
## [231,]  0.631403785 -0.361558778  0.361878282 -0.170986093  0.766157670
## [232,]  0.549070076  1.056890890  0.842823751  0.730205949 -0.680513368
## [233,]  0.670749674  0.952030579 -0.480149308  1.363986327  1.920005568
## [234,] -0.241571190 -1.694355481 -1.217364864  0.898644349 -0.371243912
## [235,] -0.147363703 -0.271539819 -0.748293256  1.812441992  1.996397990
## [236,] -0.095577104 -0.121509338 -1.863745055 -0.063215358  0.451293719
## [237,] -0.016168792  0.648185669  0.578362550 -0.536154539  1.644125985
## [238,]  1.742488219 -0.065513393  0.514708560 -0.633287869  0.484955797
## [239,] -0.612502807 -0.049163134  1.348131765  1.389657629  0.696961375
## [240,]  1.321140529 -0.928267466 -1.082491559  0.876337984  1.361122261
## [241,] -1.002015770 -0.981684591 -0.215332758 -0.950816502 -1.026281090
## [242,] -1.135123118  1.406190150  0.924914565  0.552588737  0.117166644
## [243,]  0.953767675  1.081646741 -0.979245181  1.018069642 -1.219424332
## [244,] -0.168790145 -0.087418193  0.071242736 -0.103572449  0.881802927
## [245,]  0.140801009  0.005838188  1.156654336 -1.013345799 -1.928533203
## [246,] -0.783663670 -0.530846015  0.369611151  0.302234892  0.734675726
## [247,]  0.939106896  0.677463324 -0.167050773  0.793461400 -1.216780708
## [248,] -0.846694599 -0.688639038  0.108165958 -0.891478093  1.274505218
## [249,]  0.147482248 -0.650059480  1.475261364 -0.441872405  0.650546054
## [250,] -0.741483547 -0.982374175 -0.685221666 -2.488957926 -1.399264642
## [251,]  1.122992383 -0.143105879  0.651692127  1.217106518 -1.174724278
## [252,]  1.668580762  0.548166586  1.660890246  0.048200130  0.166684609
## [253,]  0.996307645  0.809683949 -1.919119089  0.084109530 -0.226457610
## [254,]  1.545551957 -0.998004637  1.225209527 -1.547159841  0.571862343
## [255,] -0.552839919  0.877131066  0.600732669  0.260642789  0.798428740
## [256,] -0.261557340 -1.165454976  0.144548897 -0.439966236  1.048136698
## [257,] -1.069536700  1.402963452  0.943927621 -0.409918545  0.159378829
## [258,] -1.073181758  1.342934708 -1.098546879 -0.868747354  0.204758895
## [259,] -0.600194736  1.262362109  0.766492726  0.149241351 -1.265457962
## [260,] -0.212826577 -0.038598113 -1.204263615 -0.984434653  1.924131713
## [261,]  0.419588231 -1.251747843 -0.956489857  0.308651466  1.088357897
## [262,] -0.690054007  1.234892476  0.641147427 -0.319716177  0.266584212
## [263,] -0.679498838 -1.664720102 -0.130024038 -1.015582442  0.758421320
## [264,] -0.579398714 -1.109165136  0.972083154 -2.164939842  1.069072762
## [265,] -1.115184477  0.745697454  0.714744157  0.236155779  0.052200071
## [266,]  1.230013885 -0.654718891  0.928601503 -0.328130367 -0.936868087
## [267,] -0.806361592 -1.437611269 -0.422670600 -0.555456735 -1.350727643
## [268,]  1.199638233  1.365398894 -1.451597936  1.044224573 -1.219354948
## [269,]  1.510512163 -0.760237908  1.373141225  0.276027635  0.306865061
## [270,] -1.282318552  1.095903292  0.627776758  1.780594943  0.752916901
## [271,] -1.445560994 -1.567556563  0.571317737 -1.582976393 -1.220278078
## [272,] -1.059506883  1.397520302  0.938763130 -0.159542633  0.129486256
## [273,] -1.000942416  1.369078261 -1.055217975 -1.381671413  0.206547811
## [274,]  1.349569512 -0.744349805  1.049822050 -0.686110966  1.338900373
## [275,] -1.236489609  1.557382820  0.003472524 -0.001300894 -0.272338042
## [276,]  1.190827488  0.704378245 -1.660755694 -0.103424707 -1.190815669
## [277,]  0.507958459 -1.360278961  1.143217788 -0.036092454 -0.755053866
## [278,] -1.643530595 -2.078710243  0.082962561 -0.745487995 -0.545099234
## [279,]  1.187670339 -1.308224545  0.667502336 -0.899156980 -1.096201688
## [280,]  1.321568354 -0.871542686 -1.016933916 -0.635430041  1.504580181
## [281,] -1.479552599 -0.764527386  0.851152197  0.015194241 -1.399618620
## [282,] -1.341408386  0.574272317  0.877607256  0.936733255 -1.694397608
## [283,]  0.406337816 -0.237182289 -1.681378313  0.277072752 -0.983240867
## [284,]  0.838098531  0.624632591  0.442080785 -1.440176030  0.791767386
## [285,]  1.110138572  0.723389207 -1.665943947  0.584961663 -1.196129711
## [286,]  1.347062571 -1.164296557  1.137952506 -1.976003363 -0.312293829
## [287,] -1.770474306 -1.909703303  0.194979796  1.175320073 -0.608249651
## [288,]  1.067013255 -1.187422381  0.775814865  1.879173741 -1.087828074
## [289,]  1.302037219 -0.827411575 -0.996406583  1.162147281  1.362909290
## [290,] -1.412555693 -0.771571549  0.866380566 -0.883023974 -1.364661060
## [291,] -0.976313322  1.365338646  0.924284533  0.063642187  0.049529845
## [292,]  1.043137497  1.755924443 -0.983108555 -1.084228038 -0.229407121
## [293,] -0.097871730 -0.188316396  0.037250471  0.210345483  0.951421341
## [294,]  0.245752353  0.130335019  1.292630582 -1.043626202 -1.977380263
## [295,] -0.741105700 -0.513326284  0.643381723  0.344066642  1.317941365
## [296,]  0.895049825  0.694733939 -0.142739544 -1.175258426 -1.008578932
## [297,] -0.890949583 -0.658626426  0.120056913 -0.149873493  1.241824527
## [298,]  0.038802448 -0.589035354  1.507367119 -0.257632108  0.715129310
## [299,] -0.501880494  0.850767109  0.704587936 -0.842540792 -0.255485884
## [300,]  1.083771229 -0.141230565  0.645828874  1.167031247 -1.143909845
## [301,]  1.716160961  0.611602122  1.723104516  0.693000387  0.086548884
## [302,]  1.027736247  0.726430708 -1.949763452  0.933726468 -0.176037739
## [303,]  1.548147843 -0.921317538  1.282549092 -0.021314259  0.444590738
## [304,] -0.701235780  0.961399067  0.644878850  0.575005085  0.881124032
## [305,] -0.335925534 -1.040751493  0.239298355  0.060078781  1.070915097
## [306,] -1.031176032  1.284687912  0.859000879 -2.181883162  0.275433546
## [307,] -1.153985738  1.342534823 -1.117234673 -0.668274994  0.240412446
## [308,] -0.598669875  1.296466727  0.795561870  0.434506953 -1.287059829
## [309,] -0.180216802 -0.001095889 -1.173402554  0.166545170  1.804799702
##                 RC6          RC7
##   [1,] -1.406200250  1.209624174
##   [2,]  1.033828152  0.476375571
##   [3,] -0.957046637 -0.834521552
##   [4,] -1.501700427  0.270853672
##   [5,] -0.979707689  1.081471087
##   [6,]  1.367060381  1.861553048
##   [7,] -1.708099840 -1.000040311
##   [8,] -0.143895152 -1.397455558
##   [9,] -0.946360459  0.118563122
##  [10,]  0.865503971 -1.146777164
##  [11,]  0.391158797 -0.095007080
##  [12,]  0.975901569  1.094682778
##  [13,] -0.752923988 -0.688958986
##  [14,] -0.761124021 -0.429032059
##  [15,] -0.825211752  0.661321359
##  [16,]  1.108765179 -0.954110773
##  [17,]  0.900170709  1.657239539
##  [18,] -0.006380731 -0.787076834
##  [19,]  0.325991809  1.021020755
##  [20,]  0.925442120 -0.324860655
##  [21,]  0.552149654 -2.024598837
##  [22,] -0.365715696  0.554486434
##  [23,]  1.479393589 -4.184874754
##  [24,] -0.796598417 -0.218782850
##  [25,]  0.580409308  1.107855217
##  [26,] -1.505970340  0.910507638
##  [27,] -0.046960802 -0.022485134
##  [28,] -1.406374100  0.086069990
##  [29,]  0.742154540 -0.683894822
##  [30,] -1.493995349 -0.068434132
##  [31,] -0.767463506 -0.259965123
##  [32,] -0.447412540 -0.091944401
##  [33,] -1.433305535  0.024007086
##  [34,]  0.694811747  0.877609454
##  [35,] -1.539030524  0.053032332
##  [36,]  0.654263937  0.304223118
##  [37,] -0.039405422  0.787431265
##  [38,]  0.914922189 -0.822032003
##  [39,]  0.104265917 -0.825649610
##  [40,]  0.740294618 -0.108343718
##  [41,] -0.744179680  1.119911091
##  [42,] -0.414167698 -1.344992128
##  [43,]  0.585429044  0.949007246
##  [44,] -0.575894671 -2.140061505
##  [45,]  0.672051771  0.547764599
##  [46,] -0.090399469  0.844052066
##  [47,]  0.792945567  0.847133804
##  [48,] -1.047005075 -0.845754122
##  [49,]  1.693223405 -0.094381821
##  [50,]  0.125815573 -0.311421963
##  [51,]  1.452593010 -1.851982310
##  [52,]  0.689689032  0.483078336
##  [53,] -0.317780630 -2.019299421
##  [54,]  0.768120352 -2.037223796
##  [55,]  1.374867736 -0.454500152
##  [56,]  0.431918645  0.272715423
##  [57,] -0.937574412  0.125006310
##  [58,]  1.203820583  1.613617107
##  [59,]  0.238595514 -2.372612392
##  [60,] -0.765526947  1.041407866
##  [61,]  0.819950751  0.219453167
##  [62,] -1.195876122  1.103158395
##  [63,] -0.837609040  0.564499610
##  [64,]  1.574442315  0.561920682
##  [65,] -0.667010999  1.063011937
##  [66,]  0.319851780  0.254499036
##  [67,]  1.232696797  0.012729863
##  [68,] -1.589739238  0.437058447
##  [69,]  0.201973400  0.571687251
##  [70,] -1.014302030  1.362538756
##  [71,] -0.522918789  0.178839690
##  [72,] -1.195830275  0.296482973
##  [73,]  0.825905642  0.742117092
##  [74,]  0.896804113 -0.690512175
##  [75,] -0.783668630 -0.130993988
##  [76,] -0.900222533 -0.137329147
##  [77,]  1.395923999  1.420739170
##  [78,] -0.759952737 -0.565836047
##  [79,]  0.097440833  0.013212895
##  [80,] -0.907060219  0.904129818
##  [81,] -0.653967405 -0.644557549
##  [82,]  0.687397168 -1.187673627
##  [83,]  1.269655995 -0.471911216
##  [84,]  1.802006238  2.092647290
##  [85,]  0.901811505 -0.113757469
##  [86,] -1.592268177  1.090635349
##  [87,]  0.852301745  2.083037627
##  [88,] -1.615713135 -0.314676514
##  [89,]  1.290776222  0.609777612
##  [90,]  1.454828812 -2.438095683
##  [91,] -0.610943075 -1.355307035
##  [92,]  1.479207449  1.191746844
##  [93,]  0.679481134 -1.992595511
##  [94,]  1.419792385  0.380183794
##  [95,]  0.750819256 -1.262554991
##  [96,] -1.492389844 -0.897397471
##  [97,] -0.133580660  1.172198094
##  [98,] -1.304479222 -0.223903935
##  [99,] -0.842948081  0.369444365
## [100,] -0.799265219 -0.644155840
## [101,] -0.820897489 -0.210544357
## [102,]  1.477874346  1.846425192
## [103,] -0.780741873  0.167097240
## [104,]  0.204827365 -0.508429349
## [105,] -0.894913435  0.779402723
## [106,]  0.899172422 -0.420211082
## [107,]  0.708056115 -0.543330612
## [108,]  1.415928179 -0.768981982
## [109,]  1.524841861 -0.845159703
## [110,]  1.248703530 -1.012776170
## [111,] -1.544161095  0.236759930
## [112,] -0.602366786  0.008195067
## [113,] -0.867195599 -0.100541813
## [114,] -1.393079794 -0.126626591
## [115,] -0.904839913  1.423666023
## [116,]  1.337432528  1.608804178
## [117,] -1.631384091 -0.577160432
## [118,] -0.136898625 -1.398695369
## [119,] -1.099659775 -0.868612272
## [120,]  0.049210969 -0.794717861
## [121,] -1.581552335  1.344362057
## [122,]  0.947306684  0.341410124
## [123,] -0.024534499 -0.346547512
## [124,]  1.098550017  1.353621037
## [125,] -0.687347833  0.912286322
## [126,]  1.340272036 -0.117163395
## [127,] -1.558348156 -1.219057138
## [128,]  0.074258008 -0.792667912
## [129,] -1.113850259 -0.209818838
## [130,]  0.839872418 -0.105558231
## [131,] -0.891635090 -1.506905005
## [132,] -0.409983138  0.222488416
## [133,]  1.556362101 -0.457798415
## [134,] -0.585195495  1.229359353
## [135,]  0.477868144  1.550418777
## [136,] -1.484687915  1.103271533
## [137,] -0.044132641 -0.364097224
## [138,] -1.406290921 -0.116627889
## [139,]  0.468675719 -0.425567279
## [140,] -1.591528575  0.725253748
## [141,]  1.043713109 -1.437764653
## [142,] -1.574869781  0.237115505
## [143,] -0.590365453 -0.067406051
## [144,]  1.199187986 -0.006130022
## [145,] -0.351368991 -0.088772676
## [146,] -1.098182550  0.136206816
## [147,]  0.696523395 -0.362312599
## [148,]  0.942144055 -1.011636900
## [149,] -0.743087537  0.701696498
## [150,] -0.961859688 -0.256940158
## [151,] -0.776103192  1.031073418
## [152,] -0.506261380 -1.383686288
## [153,]  0.687897412  0.601202544
## [154,] -1.320270334 -0.382960241
## [155,]  0.494379216 -0.296462582
## [156,]  0.159407506  0.930874208
## [157,] -0.247528370 -1.258609849
## [158,] -0.822363956 -1.319890413
## [159,]  1.563696533 -1.400206455
## [160,]  0.312643346  0.348387723
## [161,]  1.515844076 -1.941878960
## [162,]  0.793259181  0.327998822
## [163,] -0.208493536 -0.221503746
## [164,]  0.895830490 -0.278682978
## [165,]  1.479177750  1.213988359
## [166,]  0.624290276  1.199260277
## [167,] -0.804137422 -0.223843012
## [168,]  1.147967537  0.593095374
## [169,]  0.181638528 -2.617189941
## [170,] -0.756704421 -0.240200548
## [171,]  0.663243465 -1.276052776
## [172,] -1.158258924  0.774700174
## [173,] -0.901124209 -0.737905580
## [174,]  1.644649301  0.617686689
## [175,] -0.761625247  0.891390379
## [176,]  0.288869408 -0.861950542
## [177,]  1.420064369  1.217621026
## [178,] -1.521344648  0.199624069
## [179,]  0.092950820 -0.725208405
## [180,] -1.020422305  0.791609273
## [181,] -0.612420578 -0.258355397
## [182,] -0.983511286  0.963378853
## [183,]  1.001672996  0.983848735
## [184,]  0.808680745  0.398326300
## [185,] -0.696165617  0.932225869
## [186,] -0.791555776  1.640035883
## [187,]  0.635961987  0.614134846
## [188,] -1.519951542 -1.373762814
## [189,] -0.064780583  0.287890009
## [190,] -0.960326552 -0.229723176
## [191,]  0.675199567  0.188488298
## [192,]  0.500645518 -1.198507956
## [193,]  0.432096190 -1.064246928
## [194,]  0.809016635 -0.443340324
## [195,]  0.895472339  0.595034834
## [196,] -1.410543462  1.842905421
## [197,]  0.930236159  1.797611909
## [198,] -1.582542442 -0.599999642
## [199,]  1.396660387  1.647056697
## [200,]  1.387996337 -2.458461592
## [201,] -0.511034161 -1.322302714
## [202,]  1.569813863  0.071143030
## [203,]  0.867774531  0.001179346
## [204,]  1.411360113  0.997910726
## [205,]  1.003569889  1.541017789
## [206,] -1.447124112 -0.676417176
## [207,] -0.114354509  2.074022736
## [208,] -1.530031501  0.192954216
## [209,] -0.930736167  0.693078793
## [210,] -0.966925707 -0.571961420
## [211,] -1.008596602 -0.450108973
## [212,]  1.462165524  1.479693296
## [213,] -0.711642055 -0.495796788
## [214,]  0.129611131 -0.273410744
## [215,] -1.044150048 -0.139914648
## [216,]  0.910604039 -0.203662899
## [217,]  0.680528356  0.037343310
## [218,]  1.374826723 -1.166428964
## [219,]  1.695035202  1.031092707
## [220,]  0.997373117  1.209505717
## [221,]  1.787788965 -1.419441421
## [222,]  0.222870476 -0.234197330
## [223,]  1.580404025  0.027855979
## [224,]  0.708087319  0.430005779
## [225,] -0.117468237 -1.321767008
## [226,]  0.788168310 -1.072575191
## [227,]  1.352324853  0.722225541
## [228,]  0.721813549  1.894969749
## [229,] -0.871187750 -0.630191296
## [230,]  1.068100703  0.102321621
## [231,]  0.411066313  0.489536182
## [232,] -0.826441690  0.613019578
## [233,]  0.653127208 -0.448779258
## [234,] -1.281265584  0.001873443
## [235,] -0.913780514  1.223028797
## [236,]  1.532803679  0.212224587
## [237,] -0.608269779 -0.020367966
## [238,]  0.193215478 -1.283220882
## [239,]  1.116929314 -1.607687744
## [240,] -0.284080012  1.556786886
## [241,]  1.799428978  0.268185375
## [242,] -0.815691694 -0.257669193
## [243,]  0.689256378  1.494433135
## [244,]  0.003289801  0.453340681
## [245,]  0.022058738  0.371255709
## [246,] -1.255716024 -1.524911408
## [247,]  0.713779201  1.068951726
## [248,] -1.432964347  1.058307421
## [249,]  1.219008667  0.053971092
## [250,] -1.441940680  0.096341407
## [251,] -0.647726368  0.351998978
## [252,]  1.221629490  0.155486329
## [253,]  1.004346534 -0.398843346
## [254,] -1.010520260  0.320529828
## [255,]  0.859248834  1.689483073
## [256,]  0.982496275  0.938522406
## [257,] -0.756284788 -0.239624544
## [258,] -0.825355980  0.210558338
## [259,] -0.728426560  1.318839521
## [260,] -0.459450834 -1.838859056
## [261,]  0.501658018 -0.773651327
## [262,] -0.623326308 -3.385928741
## [263,] -0.841042565  1.302386243
## [264,]  1.506322001  1.426067577
## [265,] -1.529429293  0.612798144
## [266,]  0.008993596 -0.606753228
## [267,] -1.020394451 -1.016196245
## [268,]  0.785084682 -0.459704624
## [269,]  0.264611123 -0.672717755
## [270,]  0.694337466 -0.404444687
## [271,] -0.560320121  0.197413944
## [272,] -0.754895164  0.041735962
## [273,] -0.807723390  0.140018642
## [274,]  1.322424565 -0.029776765
## [275,]  0.754197700 -0.051482194
## [276,]  0.087440778 -0.247584023
## [277,]  0.385652455  0.418955170
## [278,]  1.147363226  2.063924901
## [279,]  0.861661575  0.939927579
## [280,] -0.293282015  0.008659716
## [281,]  1.551038447 -0.563766005
## [282,] -0.606047510 -1.143422080
## [283,] -1.484263120 -1.192859501
## [284,] -1.451217353  0.342268573
## [285,]  0.014911301 -0.732308021
## [286,] -0.940601893 -0.367565711
## [287,]  0.864651807 -0.052362556
## [288,] -0.986349503 -1.415224964
## [289,] -0.403385262  0.257619317
## [290,]  1.612819345 -0.450862078
## [291,] -0.697188015  1.207808189
## [292,]  0.613465170  1.500448332
## [293,] -1.465981323  1.093224529
## [294,] -0.063401807 -0.468682322
## [295,] -1.420655976 -0.096185479
## [296,]  0.742284438 -0.549278029
## [297,] -1.504370017  0.734525430
## [298,]  1.109029964 -1.459187598
## [299,] -1.607175898  0.303124662
## [300,] -0.663148272  0.004574551
## [301,]  1.154655776  0.038972855
## [302,] -0.515291666  0.002738519
## [303,] -1.136567331  0.167460131
## [304,]  0.706106083 -0.355031420
## [305,]  0.810724080 -0.971865049
## [306,] -0.564183229  0.629725882
## [307,] -0.862513144 -0.286160759
## [308,] -0.771736720  1.041498229
## [309,] -0.521984581 -1.458868748
# Play with FA utilities

fa.parallel(data[-1]) # See factor recommendation

## Parallel analysis suggests that the number of factors =  5  and the number of components =  5
# Parallel analysis in scree plots is used to help determine the optimal number of factors/components to retain in a factor analysis by comparing the eigenvalues obtained from the data to those obtained from randomly generated data sets. Here the ideal number of factors to be considered are 7.
fa.plot(fit.pc) # See Correlations within Factors

fa.diagram(fit.pc) # Visualize the relationship

vss(data[-1]) # See Factor recommendations for a simple structure

## 
## Very Simple Structure
## Call: vss(x = data[-1])
## VSS complexity 1 achieves a maximimum of 0.59  with  8  factors
## VSS complexity 2 achieves a maximimum of 0.71  with  8  factors
## 
## The Velicer MAP achieves a minimum of 0.02  with  2  factors 
## BIC achieves a minimum of  -175.01  with  4  factors
## Sample Size adjusted BIC achieves a minimum of  -13.62  with  7  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map dof chisq    prob sqresid  fit RMSEA    BIC SABIC complex
## 1 0.31 0.00 0.024 119   681 1.1e-79    16.8 0.31 0.124   -1.1 376.4     1.0
## 2 0.38 0.45 0.024 103   474 6.8e-49    13.4 0.45 0.108 -116.9 209.7     1.3
## 3 0.45 0.53 0.029  88   371 2.0e-36    11.0 0.55 0.102 -133.5 145.6     1.5
## 4 0.50 0.59 0.030  74   249 7.8e-21     8.9 0.63 0.087 -175.0  59.7     1.5
## 5 0.53 0.63 0.035  61   179 1.4e-13     7.6 0.69 0.079 -170.5  23.0     1.6
## 6 0.55 0.64 0.044  49   124 1.7e-08     6.7 0.73 0.071 -156.5  -1.1     1.6
## 7 0.57 0.69 0.054  38    84 2.7e-05     5.6 0.77 0.062 -134.1 -13.6     1.6
## 8 0.59 0.71 0.069  28    62 2.0e-04     5.0 0.79 0.063  -98.1  -9.3     1.6
##   eChisq  SRMR eCRMS eBIC
## 1   1087 0.114 0.122  405
## 2    648 0.088 0.101   57
## 3    422 0.071 0.088  -82
## 4    233 0.053 0.071 -191
## 5    134 0.040 0.060 -216
## 6     83 0.031 0.052 -198
## 7     45 0.023 0.044 -173
## 8     30 0.019 0.041 -131
# Computing Correlation Matrix
corrm.emp <- cor(data[-1])
corrm.emp
##                            GENDER          AGE      SMOKING YELLOW_FINGERS
## GENDER                 1.00000000 -0.021306438  0.036276853   0.2129594615
## AGE                   -0.02130644  1.000000000  0.084474561   0.0052048719
## SMOKING                0.03627685  0.084474561  1.000000000   0.0145848660
## YELLOW_FINGERS         0.21295946  0.005204872  0.014584866   1.0000000000
## ANXIETY                0.15212660  0.053170355 -0.160266983   0.5658292926
## PEER_PRESSURE          0.27556432  0.018685137  0.042822324   0.3230832379
## CHRONIC_DISEASE        0.20460564 -0.012642128  0.141522309   0.0411221768
## FATIGUE                0.08356045  0.012614462  0.029575460  -0.1180579217
## ALLERGY               -0.15425095  0.027990485 -0.001912698  -0.1442995270
## WHEEZING              -0.14120674  0.055011347  0.129425926  -0.0785152929
## ALCOHOL_CONSUMING     -0.45426780  0.058985003  0.050622751  -0.2890248419
## COUGHING              -0.13330259  0.169950348  0.129471065  -0.0126398427
## SHORTNESS_OF_BREATH    0.06491069 -0.017512737 -0.061263759  -0.1059442844
## SWALLOWING_DIFFICULTY  0.07816113 -0.001269878 -0.030717735   0.3459037723
## CHEST_PAIN            -0.36295832 -0.018103926 -0.120117461  -0.1048289865
## WEIGHT                -0.01081768 -0.028273444  0.154135563   0.0006496653
## HEIGHT_INCH            0.05801867 -0.064562763  0.078120669   0.1066096672
##                            ANXIETY PEER_PRESSURE CHRONIC_DISEASE      FATIGUE
## GENDER                 0.152126604    0.27556432     0.204605643  0.083560450
## AGE                    0.053170355    0.01868514    -0.012642128  0.012614462
## SMOKING               -0.160266983    0.04282232     0.141522309  0.029575460
## YELLOW_FINGERS         0.565829293    0.32308324     0.041122177 -0.118057922
## ANXIETY                1.000000000    0.21684122    -0.009677825 -0.188538334
## PEER_PRESSURE          0.216841223    1.00000000     0.048514810  0.078148291
## CHRONIC_DISEASE       -0.009677825    0.04851481     1.000000000 -0.110528642
## FATIGUE               -0.188538334    0.07814829    -0.110528642  1.000000000
## ALLERGY               -0.165749538   -0.08179957     0.106386061  0.003056272
## WHEEZING              -0.191807339   -0.06877067    -0.049967294  0.141936883
## ALCOHOL_CONSUMING     -0.165749538   -0.15997297     0.002150491 -0.191376583
## COUGHING              -0.225644074   -0.08901867    -0.175286710  0.146856016
## SHORTNESS_OF_BREATH   -0.144076665   -0.22017534    -0.026458823  0.441744642
## SWALLOWING_DIFFICULTY  0.489402762    0.36659037     0.075176421 -0.132790075
## CHEST_PAIN            -0.113633937   -0.09482847    -0.036937848 -0.010831789
## WEIGHT                -0.049650071    0.06965455     0.060051327 -0.006639779
## HEIGHT_INCH            0.020927415    0.07121714     0.041034424  0.056616534
##                            ALLERGY    WHEEZING ALCOHOL_CONSUMING     COUGHING
## GENDER                -0.154250955 -0.14120674      -0.454267796 -0.133302586
## AGE                    0.027990485  0.05501135       0.058985003  0.169950348
## SMOKING               -0.001912698  0.12942593       0.050622751  0.129471065
## YELLOW_FINGERS        -0.144299527 -0.07851529      -0.289024842 -0.012639843
## ANXIETY               -0.165749538 -0.19180734      -0.165749538 -0.225644074
## PEER_PRESSURE         -0.081799569 -0.06877067      -0.159972971 -0.089018666
## CHRONIC_DISEASE        0.106386061 -0.04996729       0.002150491 -0.175286710
## FATIGUE                0.003056272  0.14193688      -0.191376583  0.146856016
## ALLERGY                1.000000000  0.17386692       0.344338822  0.189524168
## WHEEZING               0.173866916  1.00000000       0.265659481  0.374265392
## ALCOHOL_CONSUMING      0.344338822  0.26565948       1.000000000  0.202719970
## COUGHING               0.189524168  0.37426539       0.202719970  1.000000000
## SHORTNESS_OF_BREATH   -0.030056438  0.03783420      -0.179415842  0.277385025
## SWALLOWING_DIFFICULTY -0.061507906  0.06902742      -0.009293777 -0.157586304
## CHEST_PAIN             0.239433033  0.14764047       0.331225598  0.083957755
## WEIGHT                 0.077882001  0.04328427      -0.019123443 -0.007002533
## HEIGHT_INCH            0.055331790  0.01446635      -0.015407769 -0.020782350
##                       SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY  CHEST_PAIN
## GENDER                         0.06491069           0.078161133 -0.36295832
## AGE                           -0.01751274          -0.001269878 -0.01810393
## SMOKING                       -0.06126376          -0.030717735 -0.12011746
## YELLOW_FINGERS                -0.10594428           0.345903772 -0.10482899
## ANXIETY                       -0.14407666           0.489402762 -0.11363394
## PEER_PRESSURE                 -0.22017534           0.366590371 -0.09482847
## CHRONIC_DISEASE               -0.02645882           0.075176421 -0.03693785
## FATIGUE                        0.44174464          -0.132790075 -0.01083179
## ALLERGY                       -0.03005644          -0.061507906  0.23943303
## WHEEZING                       0.03783420           0.069027417  0.14764047
## ALCOHOL_CONSUMING             -0.17941584          -0.009293777  0.33122560
## COUGHING                       0.27738502          -0.157586304  0.08395775
## SHORTNESS_OF_BREATH            1.00000000          -0.161014804  0.02425607
## SWALLOWING_DIFFICULTY         -0.16101480           1.000000000  0.06902742
## CHEST_PAIN                     0.02425607           0.069027417  1.00000000
## WEIGHT                         0.01157763           0.050877795  0.06284525
## HEIGHT_INCH                   -0.04671399           0.092938786  0.09940380
##                              WEIGHT HEIGHT_INCH
## GENDER                -0.0108176806  0.05801867
## AGE                   -0.0282734442 -0.06456276
## SMOKING                0.1541355630  0.07812067
## YELLOW_FINGERS         0.0006496653  0.10660967
## ANXIETY               -0.0496500708  0.02092741
## PEER_PRESSURE          0.0696545532  0.07121714
## CHRONIC_DISEASE        0.0600513268  0.04103442
## FATIGUE               -0.0066397795  0.05661653
## ALLERGY                0.0778820013  0.05533179
## WHEEZING               0.0432842670  0.01446635
## ALCOHOL_CONSUMING     -0.0191234431 -0.01540777
## COUGHING              -0.0070025333 -0.02078235
## SHORTNESS_OF_BREATH    0.0115776346 -0.04671399
## SWALLOWING_DIFFICULTY  0.0508777954  0.09293879
## CHEST_PAIN             0.0628452516  0.09940380
## WEIGHT                 1.0000000000  0.49244436
## HEIGHT_INCH            0.4924443557  1.00000000
plot(corrm.emp)

data_pca <- prcomp(data[-1], scale=TRUE)
summary(data_pca)
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     1.6925 1.3991 1.29946 1.21349 1.14175 1.03533 0.97690
## Proportion of Variance 0.1685 0.1152 0.09933 0.08662 0.07668 0.06305 0.05614
## Cumulative Proportion  0.1685 0.2837 0.38299 0.46961 0.54629 0.60934 0.66548
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.94401 0.90315 0.84528 0.79577 0.76541 0.72853 0.71848
## Proportion of Variance 0.05242 0.04798 0.04203 0.03725 0.03446 0.03122 0.03037
## Cumulative Proportion  0.71790 0.76588 0.80791 0.84516 0.87962 0.91084 0.94121
##                           PC15    PC16    PC17
## Standard deviation     0.63523 0.56479 0.52625
## Proportion of Variance 0.02374 0.01876 0.01629
## Cumulative Proportion  0.96495 0.98371 1.00000
plot(data_pca)

# A table containing eigenvalues and %'s accounted, follows. Eigenvalues are the sdev^2
(eigen_data <- round(data_pca$sdev^2,3))
##  [1] 2.865 1.958 1.689 1.473 1.304 1.072 0.954 0.891 0.816 0.714 0.633 0.586
## [13] 0.531 0.516 0.404 0.319 0.277
round(fit.pc$values, 3)
##  [1] 2.865 1.958 1.689 1.473 1.304 1.072 0.954 0.891 0.816 0.714 0.633 0.586
## [13] 0.531 0.516 0.404 0.319 0.277
names(eigen_data) <- paste("PC",1:17,sep="")
eigen_data
##   PC1   PC2   PC3   PC4   PC5   PC6   PC7   PC8   PC9  PC10  PC11  PC12  PC13 
## 2.865 1.958 1.689 1.473 1.304 1.072 0.954 0.891 0.816 0.714 0.633 0.586 0.531 
##  PC14  PC15  PC16  PC17 
## 0.516 0.404 0.319 0.277
sumlambdas <- sum(eigen_data)
sumlambdas
## [1] 17.002
propvar <- round(eigen_data/sumlambdas,2)
propvar
##  PC1  PC2  PC3  PC4  PC5  PC6  PC7  PC8  PC9 PC10 PC11 PC12 PC13 PC14 PC15 PC16 
## 0.17 0.12 0.10 0.09 0.08 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.03 0.02 0.02 
## PC17 
## 0.02
cumvar_data <- cumsum(propvar)
cumvar_data
##  PC1  PC2  PC3  PC4  PC5  PC6  PC7  PC8  PC9 PC10 PC11 PC12 PC13 PC14 PC15 PC16 
## 0.17 0.29 0.39 0.48 0.56 0.62 0.68 0.73 0.78 0.82 0.86 0.89 0.92 0.95 0.97 0.99 
## PC17 
## 1.01
matlambdas <- rbind(eigen_data,propvar,cumvar_data)
matlambdas
##               PC1   PC2   PC3   PC4   PC5   PC6   PC7   PC8   PC9  PC10  PC11
## eigen_data  2.865 1.958 1.689 1.473 1.304 1.072 0.954 0.891 0.816 0.714 0.633
## propvar     0.170 0.120 0.100 0.090 0.080 0.060 0.060 0.050 0.050 0.040 0.040
## cumvar_data 0.170 0.290 0.390 0.480 0.560 0.620 0.680 0.730 0.780 0.820 0.860
##              PC12  PC13  PC14  PC15  PC16  PC17
## eigen_data  0.586 0.531 0.516 0.404 0.319 0.277
## propvar     0.030 0.030 0.030 0.020 0.020 0.020
## cumvar_data 0.890 0.920 0.950 0.970 0.990 1.010
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
rownames(matlambdas)
## [1] "Eigenvalues"         "Prop. variance"      "Cum. prop. variance"
eigvec.emp <- data_pca$rotation
print(data_pca)
## Standard deviations (1, .., p=17):
##  [1] 1.6925050 1.3991347 1.2994647 1.2134854 1.1417493 1.0353277 0.9769035
##  [8] 0.9440119 0.9031531 0.8452754 0.7957706 0.7654147 0.7285322 0.7184765
## [15] 0.6352291 0.5647943 0.5262480
## 
## Rotation (n x k) = (17 x 17):
##                                 PC1          PC2         PC3         PC4
## GENDER                 0.3210475112 -0.286879473  0.17379787 -0.07237418
## AGE                   -0.0364649541  0.030795541  0.04688999  0.27943243
## SMOKING               -0.0430283442  0.003424731  0.31567559 -0.10751874
## YELLOW_FINGERS         0.3814759828  0.128104954  0.13853036  0.29389320
## ANXIETY                0.4033326977  0.205543431 -0.07469222  0.26312783
## PEER_PRESSURE          0.3069045925  0.105788877  0.22315119  0.15097246
## CHRONIC_DISEASE        0.0902654180  0.066353796  0.10570086 -0.32228900
## FATIGUE               -0.1024499601 -0.391147209  0.29985430  0.20127738
## ALLERGY               -0.2493507498  0.239694551  0.12271547 -0.02157728
## WHEEZING              -0.2442608884  0.124539773  0.26727611  0.32565680
## ALCOHOL_CONSUMING     -0.3321543572  0.413483478 -0.08463899  0.03187039
## COUGHING              -0.2792205789 -0.058744485  0.24960914  0.42897511
## SHORTNESS_OF_BREATH   -0.1417347885 -0.424686551  0.17846341  0.18710306
## SWALLOWING_DIFFICULTY  0.2925413504  0.343624495  0.11855529  0.25354529
## CHEST_PAIN            -0.2335726303  0.316920719  0.02654379  0.06741104
## WEIGHT                -0.0003161562  0.138055198  0.49723646 -0.33025021
## HEIGHT_INCH            0.0485449546  0.155477544  0.49241846 -0.27906767
##                               PC5         PC6         PC7         PC8
## GENDER                 0.20073240 -0.24182352  0.01184223 -0.03985594
## AGE                    0.33787243  0.23970537  0.59890223 -0.53931034
## SMOKING                0.52742230  0.22454151 -0.15463295  0.20038365
## YELLOW_FINGERS        -0.02429773  0.03987572  0.14776817  0.31135018
## ANXIETY               -0.14203498  0.02100195  0.25209607  0.16394901
## PEER_PRESSURE          0.09868719 -0.13237811 -0.39679983 -0.48888049
## CHRONIC_DISEASE        0.34336849 -0.58708763  0.27268807  0.16305791
## FATIGUE               -0.19343265 -0.19872006 -0.17492007 -0.30793949
## ALLERGY                0.06195362 -0.42347967  0.18154792 -0.13304550
## WHEEZING               0.15239622 -0.07376779 -0.30344915  0.23592177
## ALCOHOL_CONSUMING      0.10964754 -0.04578332 -0.04969458 -0.01545999
## COUGHING               0.13819136  0.11156157  0.09656026  0.21956243
## SHORTNESS_OF_BREATH   -0.26321037 -0.22493715  0.29003504  0.21690138
## SWALLOWING_DIFFICULTY -0.08485041 -0.18711304 -0.12109907  0.02088317
## CHEST_PAIN            -0.36362550 -0.22121918  0.06275957 -0.11472139
## WEIGHT                -0.18496760  0.24504959  0.13211070 -0.01887354
## HEIGHT_INCH           -0.28364547  0.18977120  0.11161979 -0.01894483
##                                PC9         PC10        PC11        PC12
## GENDER                 0.281223963 -0.244510475 -0.19864542  0.05106762
## AGE                   -0.181259271 -0.179178546 -0.05135663  0.09966744
## SMOKING               -0.339753798  0.456246291  0.21657468  0.12513209
## YELLOW_FINGERS         0.158443155  0.321656428 -0.15293052  0.26549819
## ANXIETY               -0.025925593 -0.006524112  0.32378188  0.05972929
## PEER_PRESSURE          0.096840684  0.223908923 -0.20262510 -0.31742172
## CHRONIC_DISEASE       -0.258475999 -0.054485578 -0.19258350 -0.03483907
## FATIGUE               -0.196587965  0.100942472  0.31336340  0.29668046
## ALLERGY                0.539524367  0.193301357  0.42374977  0.12050452
## WHEEZING              -0.038620686 -0.568302398 -0.07283366  0.28908157
## ALCOHOL_CONSUMING     -0.031951385 -0.019777592  0.14861759 -0.21687274
## COUGHING               0.309583479  0.133044654 -0.28342941 -0.32037459
## SHORTNESS_OF_BREATH   -0.217039867  0.069598604  0.09520010 -0.35152144
## SWALLOWING_DIFFICULTY -0.312852651 -0.209578384  0.23533684 -0.25912909
## CHEST_PAIN            -0.292637073  0.281207000 -0.49725726  0.21746471
## WEIGHT                 0.003135894 -0.124979041  0.06520556 -0.37197858
## HEIGHT_INCH            0.109288894 -0.106118071 -0.05641311  0.28916542
##                              PC13        PC14        PC15        PC16
## GENDER                -0.15894162  0.55185603  0.36640789 -0.08405264
## AGE                   -0.04778967 -0.01222126 -0.04085982  0.10718595
## SMOKING               -0.17075516  0.24864171  0.03445354  0.03818447
## YELLOW_FINGERS         0.04413678 -0.28524951  0.08772850  0.24449863
## ANXIETY                0.07894326  0.02454333  0.36258509 -0.24996070
## PEER_PRESSURE          0.11049565 -0.16437026  0.05166587  0.26450112
## CHRONIC_DISEASE        0.26824464 -0.30220749 -0.07820030 -0.16153534
## FATIGUE                0.23102739 -0.15679639  0.13579435 -0.35854302
## ALLERGY               -0.27698525  0.00347222 -0.14402150  0.09185413
## WHEEZING              -0.15780709 -0.21356468  0.10523380  0.20530205
## ALCOHOL_CONSUMING      0.47755491  0.19969356  0.50074175  0.13770113
## COUGHING               0.17712228  0.07652517 -0.18263798 -0.45814232
## SHORTNESS_OF_BREATH   -0.01819713  0.11879426  0.04977730  0.51704680
## SWALLOWING_DIFFICULTY -0.12461765  0.28371676 -0.44270428 -0.11953032
## CHEST_PAIN            -0.30203928  0.21227649  0.16091658 -0.11875744
## WEIGHT                -0.33879401 -0.31881843  0.29309129 -0.17393309
## HEIGHT_INCH            0.46330708  0.27552099 -0.26518467  0.16642627
##                              PC17
## GENDER                 0.16314656
## AGE                    0.05623413
## SMOKING               -0.12035893
## YELLOW_FINGERS         0.48817125
## ANXIETY               -0.54709508
## PEER_PRESSURE         -0.29176685
## CHRONIC_DISEASE       -0.07288202
## FATIGUE                0.20916257
## ALLERGY               -0.05062214
## WHEEZING              -0.18401827
## ALCOHOL_CONSUMING      0.29244662
## COUGHING              -0.07868837
## SHORTNESS_OF_BREATH   -0.11319831
## SWALLOWING_DIFFICULTY  0.30009780
## CHEST_PAIN            -0.07706518
## WEIGHT                 0.14740550
## HEIGHT_INCH           -0.15886979
# Taking the first four PCs to generate linear combinations for all the variables with four factors
pcafactors.emp <- eigvec.emp[,1:7]
pcafactors.emp
##                                 PC1          PC2         PC3         PC4
## GENDER                 0.3210475112 -0.286879473  0.17379787 -0.07237418
## AGE                   -0.0364649541  0.030795541  0.04688999  0.27943243
## SMOKING               -0.0430283442  0.003424731  0.31567559 -0.10751874
## YELLOW_FINGERS         0.3814759828  0.128104954  0.13853036  0.29389320
## ANXIETY                0.4033326977  0.205543431 -0.07469222  0.26312783
## PEER_PRESSURE          0.3069045925  0.105788877  0.22315119  0.15097246
## CHRONIC_DISEASE        0.0902654180  0.066353796  0.10570086 -0.32228900
## FATIGUE               -0.1024499601 -0.391147209  0.29985430  0.20127738
## ALLERGY               -0.2493507498  0.239694551  0.12271547 -0.02157728
## WHEEZING              -0.2442608884  0.124539773  0.26727611  0.32565680
## ALCOHOL_CONSUMING     -0.3321543572  0.413483478 -0.08463899  0.03187039
## COUGHING              -0.2792205789 -0.058744485  0.24960914  0.42897511
## SHORTNESS_OF_BREATH   -0.1417347885 -0.424686551  0.17846341  0.18710306
## SWALLOWING_DIFFICULTY  0.2925413504  0.343624495  0.11855529  0.25354529
## CHEST_PAIN            -0.2335726303  0.316920719  0.02654379  0.06741104
## WEIGHT                -0.0003161562  0.138055198  0.49723646 -0.33025021
## HEIGHT_INCH            0.0485449546  0.155477544  0.49241846 -0.27906767
##                               PC5         PC6         PC7
## GENDER                 0.20073240 -0.24182352  0.01184223
## AGE                    0.33787243  0.23970537  0.59890223
## SMOKING                0.52742230  0.22454151 -0.15463295
## YELLOW_FINGERS        -0.02429773  0.03987572  0.14776817
## ANXIETY               -0.14203498  0.02100195  0.25209607
## PEER_PRESSURE          0.09868719 -0.13237811 -0.39679983
## CHRONIC_DISEASE        0.34336849 -0.58708763  0.27268807
## FATIGUE               -0.19343265 -0.19872006 -0.17492007
## ALLERGY                0.06195362 -0.42347967  0.18154792
## WHEEZING               0.15239622 -0.07376779 -0.30344915
## ALCOHOL_CONSUMING      0.10964754 -0.04578332 -0.04969458
## COUGHING               0.13819136  0.11156157  0.09656026
## SHORTNESS_OF_BREATH   -0.26321037 -0.22493715  0.29003504
## SWALLOWING_DIFFICULTY -0.08485041 -0.18711304 -0.12109907
## CHEST_PAIN            -0.36362550 -0.22121918  0.06275957
## WEIGHT                -0.18496760  0.24504959  0.13211070
## HEIGHT_INCH           -0.28364547  0.18977120  0.11161979
# Multiplying each column of the eigenvector’s matrix by the square-root of the corresponding eigenvalue in order to get the factor loadings
unrot.fact.emp <- sweep(pcafactors.emp,MARGIN=2,data_pca$sdev[1:7],`*`)
unrot.fact.emp
##                                PC1          PC2         PC3         PC4
## GENDER                 0.543374530 -0.401383018  0.22584419 -0.08782501
## AGE                   -0.061717118  0.043087109  0.06093188  0.33908718
## SMOKING               -0.072825689  0.004791661  0.41020928 -0.13047242
## YELLOW_FINGERS         0.645650022  0.179236082  0.18001531  0.35663511
## ANXIETY                0.682642622  0.287582941 -0.09705991  0.31930178
## PEER_PRESSURE          0.519437569  0.148012887  0.28997708  0.18320288
## CHRONIC_DISEASE        0.152774675  0.092837896  0.13735453 -0.39109300
## FATIGUE               -0.173397073 -0.547267624  0.38965007  0.24424716
## ALLERGY               -0.422027400  0.335364958  0.15946442 -0.02618371
## WHEEZING              -0.413412784  0.174247914  0.34731586  0.39517978
## ALCOHOL_CONSUMING     -0.562172923  0.578519071 -0.10998537  0.03867426
## COUGHING              -0.472582236 -0.082191446  0.32435826  0.52055504
## SHORTNESS_OF_BREATH   -0.239886844 -0.594193680  0.23190689  0.22704683
## SWALLOWING_DIFFICULTY  0.495127709  0.480776946  0.15405841  0.30767351
## CHEST_PAIN            -0.395322853  0.443414767  0.03449271  0.08180231
## WEIGHT                -0.000535096  0.193157814  0.64614121 -0.40075381
## HEIGHT_INCH            0.082162580  0.217534023  0.63988039 -0.33864455
##                               PC5         PC6         PC7
## GENDER                 0.22918608 -0.25036659  0.01156872
## AGE                    0.38576562  0.24817361  0.58506968
## SMOKING                0.60218404  0.23247405 -0.15106147
## YELLOW_FINGERS        -0.02774191  0.04128444  0.14435524
## ANXIETY               -0.16216833  0.02174391  0.24627354
## PEER_PRESSURE          0.11267604 -0.13705473 -0.38763515
## CHRONIC_DISEASE        0.39204073 -0.60782810  0.26638993
## FATIGUE               -0.22085159 -0.20574039 -0.17088003
## ALLERGY                0.07073550 -0.43844025  0.17735480
## WHEEZING               0.17399828 -0.07637384 -0.29644054
## ALCOHOL_CONSUMING      0.12519000 -0.04740074 -0.04854681
## COUGHING               0.15777989  0.11550278  0.09433005
## SHORTNESS_OF_BREATH   -0.30052025 -0.23288367  0.28333624
## SWALLOWING_DIFFICULTY -0.09687790 -0.19372331 -0.11830211
## CHEST_PAIN            -0.41516916 -0.22903435  0.06131004
## WEIGHT                -0.21118663  0.25370663  0.12905941
## HEIGHT_INCH           -0.32385202  0.19647538  0.10904177
# Computing communalities
communalities.emp <- rowSums(unrot.fact.emp^2)
communalities.emp
##                GENDER                   AGE               SMOKING 
##             0.6304266             0.6770701             0.6301106 
##        YELLOW_FINGERS               ANXIETY         PEER_PRESSURE 
##             0.6318961             0.7475012             0.5911141 
##       CHRONIC_DISEASE               FATIGUE               ALLERGY 
##             0.7978935             0.6613568             0.5453794 
##              WHEEZING     ALCOHOL_CONSUMING              COUGHING 
##             0.6020532             0.6845913             0.6534088 
##   SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY            CHEST_PAIN 
##             0.7407695             0.6556043             0.5893593 
##                WEIGHT           HEIGHT_INCH 
##             0.7410355             0.7335716
# Performing the varimax rotation. The default in the varimax function is norm=TRUE thus, Kaiser normalization is carried out
rot.fact.emp <- varimax(unrot.fact.emp)
#View(unrot.fact.emp)
rot.fact.emp
## $loadings
## 
## Loadings:
##                       PC1    PC2    PC3    PC4    PC5    PC6    PC7   
## GENDER                 0.238 -0.209                0.608 -0.391       
## AGE                                                              0.812
## SMOKING               -0.146  0.229  0.223  0.605  0.300 -0.163  0.154
## YELLOW_FINGERS         0.739                       0.202         0.182
## ANXIETY                0.752  0.124        -0.349                0.180
## PEER_PRESSURE          0.594                0.293  0.241        -0.289
## CHRONIC_DISEASE                                          -0.886       
## FATIGUE                      -0.747         0.231  0.111        -0.167
## ALLERGY                                     0.162 -0.568 -0.421       
## WHEEZING                     -0.155         0.681 -0.325              
## ALCOHOL_CONSUMING     -0.178  0.333         0.276 -0.674              
## COUGHING                     -0.354         0.517 -0.212  0.178  0.421
## SHORTNESS_OF_BREATH   -0.174 -0.823        -0.104                0.147
## SWALLOWING_DIFFICULTY  0.775  0.122               -0.135        -0.123
## CHEST_PAIN                           0.117        -0.744              
## WEIGHT                               0.857                            
## HEIGHT_INCH            0.105         0.845                            
## 
##                  PC1   PC2   PC3   PC4   PC5   PC6   PC7
## SS loadings    2.242 1.646 1.536 1.499 2.084 1.204 1.104
## Proportion Var 0.132 0.097 0.090 0.088 0.123 0.071 0.065
## Cumulative Var 0.132 0.229 0.319 0.407 0.530 0.601 0.665
## 
## $rotmat
##             [,1]       [,2]        [,3]        [,4]        [,5]        [,6]
## [1,]  0.70815628  0.1699665  0.04580533 -0.31954248  0.58522523 -0.10011041
## [2,]  0.39609235  0.6252274  0.19449972  0.08889326 -0.63442845 -0.06041631
## [3,]  0.19809174 -0.3742450  0.72472125  0.50604385  0.06650229 -0.18126731
## [4,]  0.50904583 -0.3693835 -0.46089827  0.31168727 -0.16948204  0.37431575
## [5,] -0.12631412  0.4006414 -0.30071113  0.54231982  0.35115658 -0.43405319
## [6,] -0.16382089  0.3545694  0.32220784  0.06024877  0.29351376  0.73731900
## [7,] -0.02156387 -0.1321573  0.16786469 -0.48889729 -0.11137317 -0.28515993
##             [,7]
## [1,] -0.11362166
## [2,]  0.01788165
## [3,]  0.04602938
## [4,]  0.35498673
## [5,]  0.35676335
## [6,]  0.33197262
## [7,]  0.78813081
# The print method of varimax omits loadings less than abs(0.1). In order to display all the loadings, it is necessary to ask explicitly the contents of the object $loadings
fact.load.emp <- rot.fact.emp$loadings[1:17,1:7]
fact.load.emp
##                               PC1          PC2           PC3         PC4
## GENDER                 0.23765663 -0.209159915  0.0033261366 -0.01884640
## AGE                    0.05604210  0.033619981 -0.0444005987  0.09819627
## SMOKING               -0.14572238  0.228945489  0.2234816958  0.60505029
## YELLOW_FINGERS         0.73904640  0.007143313  0.0764006060 -0.07125801
## ANXIETY                0.75225097  0.124402050 -0.0331910366 -0.34920292
## PEER_PRESSURE          0.59374924  0.052410233  0.0351828377  0.29338095
## CHRONIC_DISEASE        0.01739553  0.083415576  0.0358321430 -0.04720338
## FATIGUE               -0.07275521 -0.746532380  0.0268653287  0.23144306
## ALLERGY               -0.08869966 -0.062614741  0.0407643367  0.16243972
## WHEEZING               0.04314803 -0.155467975 -0.0421692024  0.68121223
## ALCOHOL_CONSUMING     -0.17806070  0.332796520 -0.0718305634  0.27623302
## COUGHING              -0.07886413 -0.353684875 -0.0368821757  0.51650207
## SHORTNESS_OF_BREATH   -0.17371553 -0.823355508 -0.0002412482 -0.10357448
## SWALLOWING_DIFFICULTY  0.77472151  0.121577811  0.0328880238  0.05200891
## CHEST_PAIN             0.03279694 -0.088726836  0.1167723267 -0.06023722
## WEIGHT                -0.01754703  0.015183692  0.8574405826  0.05706536
## HEIGHT_INCH            0.10508588 -0.038904241  0.8448854669 -0.00576498
##                                PC5          PC6           PC7
## GENDER                 0.608254923 -0.391337749 -0.0819297480
## AGE                    0.026274259 -0.031842028  0.8120842984
## SMOKING                0.300252608 -0.163089995  0.1538819759
## YELLOW_FINGERS         0.201964885  0.026715113  0.1823107522
## ANXIETY                0.078485650  0.067593675  0.1799181806
## PEER_PRESSURE          0.240830561 -0.084353585 -0.2887975316
## CHRONIC_DISEASE        0.035519303 -0.886486884 -0.0001753085
## FATIGUE                0.111333251  0.064110653 -0.1672122736
## ALLERGY               -0.568305310 -0.421266614  0.0714579660
## WHEEZING              -0.324666611  0.068521079  0.0094470657
## ALCOHOL_CONSUMING     -0.674440271 -0.019704464  0.0735524063
## COUGHING              -0.212275352  0.178110887  0.4209242675
## SHORTNESS_OF_BREATH    0.008087243 -0.019199701  0.1466847304
## SWALLOWING_DIFFICULTY -0.134861337 -0.058423617 -0.1234597788
## CHEST_PAIN            -0.744080438  0.031004891 -0.0923573052
## WEIGHT                -0.026034468 -0.036822680  0.0015896778
## HEIGHT_INCH           -0.058177346 -0.009777632 -0.0605815125
# Computing the rotated factor scores for the 30 European Countries. Notice that signs are reversed for factors F2 (PC2), F3 (PC3) and F4 (PC4)
scale.emp <- scale(data[-1])
scale.emp
##            GENDER         AGE    SMOKING YELLOW_FINGERS    ANXIETY
##   [1,] -0.9510367  0.77060032  1.1334539      0.8678918  1.0016168
##   [2,] -0.9510367  1.37959136 -0.8794039     -1.1484884 -0.9951548
##   [3,]  1.0480813 -0.44738177  1.1334539     -1.1484884 -0.9951548
##   [4,] -0.9510367  0.03981106 -0.8794039      0.8678918  1.0016168
##   [5,]  1.0480813  0.03981106  1.1334539      0.8678918 -0.9951548
##   [6,]  1.0480813  1.50138957  1.1334539      0.8678918 -0.9951548
##   [7,] -0.9510367 -1.29996923 -0.8794039     -1.1484884 -0.9951548
##   [8,]  1.0480813 -1.42176744 -0.8794039      0.8678918  1.0016168
##   [9,]  1.0480813  0.64880211 -0.8794039     -1.1484884  1.0016168
##  [10,] -0.9510367 -1.17817102 -0.8794039      0.8678918  1.0016168
##  [11,]  1.0480813 -0.20378535 -0.8794039      0.8678918  1.0016168
##  [12,] -0.9510367  1.13599494  1.1334539     -1.1484884 -0.9951548
##  [13,]  1.0480813 -0.32558356 -0.8794039     -1.1484884 -0.9951548
##  [14,] -0.9510367 -0.56917998 -0.8794039     -1.1484884 -0.9951548
##  [15,] -0.9510367  0.77060032 -0.8794039     -1.1484884 -0.9951548
##  [16,]  1.0480813 -1.78716206  1.1334539      0.8678918  1.0016168
##  [17,] -0.9510367  1.50138957 -0.8794039     -1.1484884 -0.9951548
##  [18,] -0.9510367 -0.69097819 -0.8794039      0.8678918  1.0016168
##  [19,]  1.0480813  0.64880211 -0.8794039      0.8678918  1.0016168
##  [20,]  1.0480813 -0.20378535  1.1334539     -1.1484884 -0.9951548
##  [21,]  1.0480813 -2.27435490 -0.8794039      0.8678918  1.0016168
##  [22,]  1.0480813  0.16160927  1.1334539      0.8678918  1.0016168
##  [23,]  1.0480813 -5.07571369 -0.8794039     -1.1484884 -0.9951548
##  [24,] -0.9510367 -0.32558356 -0.8794039     -1.1484884 -0.9951548
##  [25,] -0.9510367  1.13599494 -0.8794039      0.8678918  1.0016168
##  [26,] -0.9510367  0.28340748  1.1334539      0.8678918  1.0016168
##  [27,]  1.0480813 -0.20378535 -0.8794039      0.8678918  1.0016168
##  [28,] -0.9510367  0.77060032  1.1334539     -1.1484884 -0.9951548
##  [29,]  1.0480813 -1.17817102 -0.8794039      0.8678918  1.0016168
##  [30,] -0.9510367 -0.93457460  1.1334539      0.8678918 -0.9951548
##  [31,]  1.0480813 -0.69097819 -0.8794039      0.8678918 -0.9951548
##  [32,] -0.9510367 -0.08198714 -0.8794039     -1.1484884  1.0016168
##  [33,] -0.9510367 -0.81277639 -0.8794039      0.8678918  1.0016168
##  [34,]  1.0480813  0.52700390 -0.8794039      0.8678918  1.0016168
##  [35,] -0.9510367 -0.44738177  1.1334539      0.8678918  1.0016168
##  [36,]  1.0480813 -0.44738177 -0.8794039      0.8678918  1.0016168
##  [37,] -0.9510367 -0.32558356  1.1334539      0.8678918 -0.9951548
##  [38,]  1.0480813 -0.81277639  1.1334539     -1.1484884 -0.9951548
##  [39,] -0.9510367 -0.81277639 -0.8794039     -1.1484884 -0.9951548
##  [40,] -0.9510367 -0.32558356 -0.8794039     -1.1484884 -0.9951548
##  [41,] -0.9510367  0.64880211 -0.8794039     -1.1484884  1.0016168
##  [42,] -0.9510367  0.03981106  1.1334539     -1.1484884 -0.9951548
##  [43,]  1.0480813  1.74498598  1.1334539      0.8678918  1.0016168
##  [44,] -0.9510367 -1.29996923 -0.8794039     -1.1484884 -0.9951548
##  [45,]  1.0480813  0.89239852 -0.8794039      0.8678918 -0.9951548
##  [46,] -0.9510367  1.13599494 -0.8794039      0.8678918  1.0016168
##  [47,] -0.9510367 -0.08198714 -0.8794039      0.8678918 -0.9951548
##  [48,]  1.0480813  0.16160927 -0.8794039      0.8678918 -0.9951548
##  [49,]  1.0480813  0.89239852  1.1334539     -1.1484884  1.0016168
##  [50,] -0.9510367 -0.32558356  1.1334539     -1.1484884  1.0016168
##  [51,]  1.0480813 -0.81277639  1.1334539     -1.1484884 -0.9951548
##  [52,] -0.9510367  0.03981106 -0.8794039      0.8678918  1.0016168
##  [53,]  1.0480813 -1.05637281 -0.8794039     -1.1484884 -0.9951548
##  [54,] -0.9510367 -1.66536385 -0.8794039     -1.1484884 -0.9951548
##  [55,]  1.0480813 -0.69097819  1.1334539      0.8678918 -0.9951548
##  [56,] -0.9510367 -1.29996923  1.1334539      0.8678918  1.0016168
##  [57,]  1.0480813  0.03981106  1.1334539      0.8678918 -0.9951548
##  [58,] -0.9510367  1.25779315  1.1334539     -1.1484884 -0.9951548
##  [59,] -0.9510367 -1.90896027  1.1334539      0.8678918 -0.9951548
##  [60,] -0.9510367  0.77060032 -0.8794039      0.8678918  1.0016168
##  [61,] -0.9510367  0.89239852  1.1334539      0.8678918 -0.9951548
##  [62,]  1.0480813 -0.32558356  1.1334539      0.8678918  1.0016168
##  [63,] -0.9510367  0.89239852  1.1334539      0.8678918 -0.9951548
##  [64,]  1.0480813  0.64880211  1.1334539     -1.1484884  1.0016168
##  [65,] -0.9510367  1.37959136  1.1334539      0.8678918 -0.9951548
##  [66,]  1.0480813  1.01419673 -0.8794039      0.8678918  1.0016168
##  [67,]  1.0480813 -0.81277639  1.1334539      0.8678918 -0.9951548
##  [68,] -0.9510367  0.40520569 -0.8794039     -1.1484884 -0.9951548
##  [69,]  1.0480813  1.62318777 -0.8794039      0.8678918  1.0016168
##  [70,]  1.0480813  1.86678419 -0.8794039      0.8678918  1.0016168
##  [71,] -0.9510367  0.64880211 -0.8794039      0.8678918  1.0016168
##  [72,]  1.0480813  0.40520569 -0.8794039      0.8678918  1.0016168
##  [73,] -0.9510367  0.52700390  1.1334539     -1.1484884 -0.9951548
##  [74,]  1.0480813 -0.32558356 -0.8794039     -1.1484884 -0.9951548
##  [75,] -0.9510367 -0.20378535 -0.8794039     -1.1484884 -0.9951548
##  [76,] -0.9510367 -0.56917998 -0.8794039     -1.1484884 -0.9951548
##  [77,]  1.0480813  1.62318777  1.1334539      0.8678918  1.0016168
##  [78,] -0.9510367 -0.81277639 -0.8794039     -1.1484884 -0.9951548
##  [79,] -0.9510367  0.52700390 -0.8794039      0.8678918  1.0016168
##  [80,]  1.0480813  1.25779315 -0.8794039      0.8678918  1.0016168
##  [81,]  1.0480813 -0.56917998  1.1334539     -1.1484884 -0.9951548
##  [82,]  1.0480813 -1.05637281 -0.8794039      0.8678918  1.0016168
##  [83,]  1.0480813 -0.08198714 -0.8794039      0.8678918  1.0016168
##  [84,]  1.0480813  2.23217882  1.1334539     -1.1484884 -0.9951548
##  [85,] -0.9510367 -0.81277639  1.1334539     -1.1484884 -0.9951548
##  [86,] -0.9510367 -0.32558356  1.1334539      0.8678918  1.0016168
##  [87,] -0.9510367  0.40520569  1.1334539      0.8678918  1.0016168
##  [88,] -0.9510367 -0.08198714  1.1334539      0.8678918  1.0016168
##  [89,]  1.0480813 -0.08198714 -0.8794039      0.8678918  1.0016168
##  [90,]  1.0480813 -0.93457460 -0.8794039     -1.1484884 -0.9951548
##  [91,]  1.0480813 -0.08198714  1.1334539     -1.1484884 -0.9951548
##  [92,]  1.0480813  1.01419673  1.1334539     -1.1484884 -0.9951548
##  [93,] -0.9510367 -1.29996923 -0.8794039     -1.1484884 -0.9951548
##  [94,]  1.0480813 -0.44738177  1.1334539      0.8678918  1.0016168
##  [95,] -0.9510367 -1.78716206 -0.8794039     -1.1484884 -0.9951548
##  [96,] -0.9510367 -0.32558356  1.1334539      0.8678918  1.0016168
##  [97,]  1.0480813 -0.20378535 -0.8794039      0.8678918  1.0016168
##  [98,] -0.9510367 -0.44738177 -0.8794039     -1.1484884 -0.9951548
##  [99,] -0.9510367  0.16160927  1.1334539      0.8678918  1.0016168
## [100,] -0.9510367 -0.81277639 -0.8794039     -1.1484884 -0.9951548
## [101,] -0.9510367 -0.56917998 -0.8794039     -1.1484884 -0.9951548
## [102,]  1.0480813  2.23217882  1.1334539      0.8678918  1.0016168
## [103,] -0.9510367  0.16160927 -0.8794039     -1.1484884 -0.9951548
## [104,] -0.9510367 -0.08198714 -0.8794039      0.8678918  1.0016168
## [105,]  1.0480813  1.13599494 -0.8794039      0.8678918  1.0016168
## [106,]  1.0480813 -0.32558356  1.1334539     -1.1484884 -0.9951548
## [107,]  1.0480813 -0.20378535 -0.8794039      0.8678918  1.0016168
## [108,]  1.0480813 -0.32558356 -0.8794039      0.8678918  1.0016168
## [109,]  1.0480813 -1.66536385  1.1334539     -1.1484884 -0.9951548
## [110,] -0.9510367 -1.17817102  1.1334539     -1.1484884 -0.9951548
## [111,] -0.9510367 -0.56917998  1.1334539      0.8678918  1.0016168
## [112,] -0.9510367 -0.20378535 -0.8794039      0.8678918  1.0016168
## [113,]  1.0480813  0.64880211  1.1334539     -1.1484884 -0.9951548
## [114,] -0.9510367 -0.32558356 -0.8794039      0.8678918  1.0016168
## [115,]  1.0480813  1.13599494  1.1334539      0.8678918 -0.9951548
## [116,]  1.0480813  1.13599494  1.1334539      0.8678918 -0.9951548
## [117,] -0.9510367 -0.69097819 -0.8794039     -1.1484884 -0.9951548
## [118,]  1.0480813 -1.42176744 -0.8794039      0.8678918  1.0016168
## [119,]  1.0480813 -1.05637281 -0.8794039      0.8678918  1.0016168
## [120,]  1.0480813 -0.81277639  1.1334539      0.8678918  1.0016168
## [121,] -0.9510367  1.74498598 -0.8794039      0.8678918  1.0016168
## [122,] -0.9510367  0.16160927  1.1334539     -1.1484884 -0.9951548
## [123,] -0.9510367 -0.69097819 -0.8794039     -1.1484884  1.0016168
## [124,]  1.0480813  0.40520569 -0.8794039      0.8678918  1.0016168
## [125,] -0.9510367  0.89239852 -0.8794039     -1.1484884 -0.9951548
## [126,]  1.0480813 -1.17817102  1.1334539      0.8678918  1.0016168
## [127,] -0.9510367 -1.42176744 -0.8794039     -1.1484884 -0.9951548
## [128,] -0.9510367 -0.56917998 -0.8794039      0.8678918  1.0016168
## [129,]  1.0480813 -0.56917998 -0.8794039      0.8678918  1.0016168
## [130,]  1.0480813  0.03981106  1.1334539     -1.1484884 -0.9951548
## [131,]  1.0480813 -1.42176744 -0.8794039      0.8678918  1.0016168
## [132,]  1.0480813 -0.20378535  1.1334539      0.8678918  1.0016168
## [133,]  1.0480813 -0.20378535 -0.8794039     -1.1484884 -0.9951548
## [134,] -0.9510367  1.62318777 -0.8794039     -1.1484884 -0.9951548
## [135,] -0.9510367  1.01419673 -0.8794039      0.8678918  1.0016168
## [136,] -0.9510367  0.77060032  1.1334539     -1.1484884  1.0016168
## [137,]  1.0480813 -0.81277639 -0.8794039      0.8678918  1.0016168
## [138,] -0.9510367  0.52700390  1.1334539     -1.1484884 -0.9951548
## [139,]  1.0480813 -1.05637281 -0.8794039      0.8678918  1.0016168
## [140,] -0.9510367  0.03981106  1.1334539      0.8678918 -0.9951548
## [141,]  1.0480813 -1.90896027 -0.8794039      0.8678918 -0.9951548
## [142,] -0.9510367 -0.08198714 -0.8794039     -1.1484884  1.0016168
## [143,] -0.9510367  0.28340748 -0.8794039      0.8678918  1.0016168
## [144,]  1.0480813  0.03981106 -0.8794039      0.8678918  1.0016168
## [145,] -0.9510367  0.16160927  1.1334539      0.8678918  1.0016168
## [146,]  1.0480813  0.28340748 -0.8794039      0.8678918  1.0016168
## [147,] -0.9510367 -1.42176744  1.1334539      0.8678918 -0.9951548
## [148,]  1.0480813 -0.81277639  1.1334539     -1.1484884 -0.9951548
## [149,] -0.9510367  0.89239852 -0.8794039     -1.1484884 -0.9951548
## [150,] -0.9510367 -0.56917998 -0.8794039     -1.1484884 -0.9951548
## [151,] -0.9510367  0.52700390 -0.8794039     -1.1484884  1.0016168
## [152,] -0.9510367 -0.08198714  1.1334539     -1.1484884 -0.9951548
## [153,]  1.0480813  1.37959136  1.1334539      0.8678918  1.0016168
## [154,] -0.9510367  0.77060032 -0.8794039     -1.1484884 -0.9951548
## [155,]  1.0480813  0.16160927 -0.8794039      0.8678918 -0.9951548
## [156,] -0.9510367  1.50138957 -0.8794039      0.8678918  1.0016168
## [157,] -0.9510367 -1.90896027 -0.8794039      0.8678918 -0.9951548
## [158,]  1.0480813 -0.69097819 -0.8794039      0.8678918 -0.9951548
## [159,]  1.0480813 -0.81277639  1.1334539     -1.1484884  1.0016168
## [160,] -0.9510367  0.64880211  1.1334539     -1.1484884  1.0016168
## [161,]  1.0480813 -0.93457460  1.1334539     -1.1484884 -0.9951548
## [162,] -0.9510367 -0.08198714 -0.8794039      0.8678918  1.0016168
## [163,]  1.0480813  1.25779315 -0.8794039     -1.1484884 -0.9951548
## [164,] -0.9510367  0.64880211 -0.8794039     -1.1484884 -0.9951548
## [165,]  1.0480813  1.50138957  1.1334539      0.8678918 -0.9951548
## [166,] -0.9510367  0.03981106  1.1334539      0.8678918  1.0016168
## [167,]  1.0480813 -0.20378535  1.1334539      0.8678918 -0.9951548
## [168,] -0.9510367 -0.08198714  1.1334539     -1.1484884 -0.9951548
## [169,] -0.9510367 -2.27435490  1.1334539      0.8678918 -0.9951548
## [170,] -0.9510367 -0.81277639 -0.8794039      0.8678918  1.0016168
## [171,] -0.9510367 -1.05637281  1.1334539      0.8678918 -0.9951548
## [172,]  1.0480813 -0.69097819  1.1334539      0.8678918  1.0016168
## [173,] -0.9510367 -0.81277639  1.1334539      0.8678918 -0.9951548
## [174,]  1.0480813  0.77060032  1.1334539     -1.1484884  1.0016168
## [175,] -0.9510367  1.13599494  1.1334539      0.8678918 -0.9951548
## [176,]  1.0480813 -0.44738177 -0.8794039      0.8678918  1.0016168
## [177,]  1.0480813  0.89239852  1.1334539      0.8678918 -0.9951548
## [178,] -0.9510367  0.16160927 -0.8794039     -1.1484884 -0.9951548
## [179,]  1.0480813 -0.20378535 -0.8794039      0.8678918  1.0016168
## [180,]  1.0480813  1.13599494 -0.8794039      0.8678918  1.0016168
## [181,] -0.9510367  0.03981106 -0.8794039      0.8678918  1.0016168
## [182,]  1.0480813  1.37959136 -0.8794039      0.8678918  1.0016168
## [183,] -0.9510367  1.01419673  1.1334539     -1.1484884 -0.9951548
## [184,]  1.0480813  1.01419673 -0.8794039     -1.1484884 -0.9951548
## [185,] -0.9510367  1.13599494 -0.8794039     -1.1484884 -0.9951548
## [186,] -0.9510367  1.74498598 -0.8794039     -1.1484884 -0.9951548
## [187,]  1.0480813  1.13599494  1.1334539      0.8678918  1.0016168
## [188,] -0.9510367 -0.93457460 -0.8794039     -1.1484884 -0.9951548
## [189,] -0.9510367  0.28340748 -0.8794039      0.8678918  1.0016168
## [190,]  1.0480813  0.52700390 -0.8794039      0.8678918  1.0016168
## [191,]  1.0480813  0.77060032  1.1334539     -1.1484884 -0.9951548
## [192,]  1.0480813 -0.93457460 -0.8794039      0.8678918  1.0016168
## [193,]  1.0480813 -1.42176744 -0.8794039      0.8678918  1.0016168
## [194,]  1.0480813  0.16160927  1.1334539     -1.1484884 -0.9951548
## [195,] -0.9510367  0.03981106  1.1334539     -1.1484884 -0.9951548
## [196,] -0.9510367  0.77060032  1.1334539      0.8678918  1.0016168
## [197,] -0.9510367  0.16160927  1.1334539      0.8678918  1.0016168
## [198,] -0.9510367 -0.44738177  1.1334539      0.8678918  1.0016168
## [199,]  1.0480813  1.25779315 -0.8794039      0.8678918  1.0016168
## [200,]  1.0480813 -0.93457460 -0.8794039     -1.1484884 -0.9951548
## [201,]  1.0480813  0.03981106  1.1334539     -1.1484884 -0.9951548
## [202,]  1.0480813 -0.32558356  1.1334539     -1.1484884 -0.9951548
## [203,] -0.9510367  1.37959136 -0.8794039     -1.1484884 -0.9951548
## [204,]  1.0480813  0.28340748  1.1334539      0.8678918  1.0016168
## [205,] -0.9510367  1.98858240 -0.8794039     -1.1484884 -0.9951548
## [206,] -0.9510367 -0.08198714  1.1334539      0.8678918  1.0016168
## [207,]  1.0480813  1.01419673 -0.8794039      0.8678918  1.0016168
## [208,] -0.9510367  0.03981106 -0.8794039     -1.1484884 -0.9951548
## [209,] -0.9510367  0.52700390  1.1334539      0.8678918  1.0016168
## [210,] -0.9510367 -0.93457460 -0.8794039     -1.1484884 -0.9951548
## [211,] -0.9510367 -1.05637281 -0.8794039     -1.1484884 -0.9951548
## [212,]  1.0480813  1.74498598  1.1334539      0.8678918  1.0016168
## [213,] -0.9510367 -0.56917998 -0.8794039     -1.1484884 -0.9951548
## [214,] -0.9510367  0.16160927 -0.8794039      0.8678918  1.0016168
## [215,]  1.0480813 -0.20378535 -0.8794039      0.8678918  1.0016168
## [216,]  1.0480813 -0.08198714  1.1334539     -1.1484884 -0.9951548
## [217,]  1.0480813  0.52700390 -0.8794039      0.8678918  1.0016168
## [218,]  1.0480813 -0.81277639 -0.8794039      0.8678918  1.0016168
## [219,]  1.0480813  0.89239852  1.1334539     -1.1484884 -0.9951548
## [220,] -0.9510367  0.89239852  1.1334539     -1.1484884 -0.9951548
## [221,]  1.0480813 -0.69097819  1.1334539     -1.1484884  1.0016168
## [222,] -0.9510367 -0.20378535  1.1334539     -1.1484884  1.0016168
## [223,]  1.0480813  1.74498598  1.1334539     -1.1484884 -0.9951548
## [224,] -0.9510367  0.03981106 -0.8794039      0.8678918  1.0016168
## [225,]  1.0480813 -0.08198714 -0.8794039     -1.1484884 -0.9951548
## [226,] -0.9510367 -0.44738177 -0.8794039     -1.1484884 -0.9951548
## [227,]  1.0480813  0.89239852  1.1334539      0.8678918 -0.9951548
## [228,] -0.9510367  1.01419673  1.1334539      0.8678918  1.0016168
## [229,]  1.0480813 -0.81277639  1.1334539      0.8678918 -0.9951548
## [230,] -0.9510367 -0.69097819  1.1334539     -1.1484884 -0.9951548
## [231,] -0.9510367  1.86678419  1.1334539      0.8678918 -0.9951548
## [232,] -0.9510367  0.16160927 -0.8794039      0.8678918  1.0016168
## [233,] -0.9510367 -0.08198714  1.1334539      0.8678918 -0.9951548
## [234,]  1.0480813 -1.66536385  1.1334539      0.8678918  1.0016168
## [235,] -0.9510367  1.74498598  1.1334539      0.8678918 -0.9951548
## [236,]  1.0480813  0.16160927  1.1334539     -1.1484884  1.0016168
## [237,] -0.9510367  0.03981106  1.1334539      0.8678918 -0.9951548
## [238,]  1.0480813 -1.05637281 -0.8794039      0.8678918  1.0016168
## [239,]  1.0480813 -3.00514415  1.1334539      0.8678918 -0.9951548
## [240,]  1.0480813  1.50138957  1.1334539      0.8678918  1.0016168
## [241,]  1.0480813  0.89239852 -0.8794039     -1.1484884 -0.9951548
## [242,] -0.9510367 -0.44738177 -0.8794039     -1.1484884 -0.9951548
## [243,] -0.9510367  1.74498598 -0.8794039      0.8678918  1.0016168
## [244,] -0.9510367 -0.20378535  1.1334539     -1.1484884  1.0016168
## [245,]  1.0480813  0.16160927 -0.8794039      0.8678918  1.0016168
## [246,] -0.9510367 -0.44738177  1.1334539     -1.1484884 -0.9951548
## [247,]  1.0480813  1.01419673 -0.8794039      0.8678918  1.0016168
## [248,] -0.9510367  0.52700390  1.1334539      0.8678918 -0.9951548
## [249,]  1.0480813  0.16160927 -0.8794039      0.8678918 -0.9951548
## [250,] -0.9510367  0.64880211 -0.8794039     -1.1484884  1.0016168
## [251,] -0.9510367  0.77060032 -0.8794039      0.8678918  1.0016168
## [252,]  1.0480813  0.16160927 -0.8794039      0.8678918  1.0016168
## [253,] -0.9510367 -0.44738177  1.1334539      0.8678918  1.0016168
## [254,]  1.0480813  0.52700390 -0.8794039      0.8678918  1.0016168
## [255,] -0.9510367  1.37959136  1.1334539      0.8678918 -0.9951548
## [256,]  1.0480813  1.74498598  1.1334539     -1.1484884 -0.9951548
## [257,] -0.9510367 -0.32558356 -0.8794039     -1.1484884 -0.9951548
## [258,] -0.9510367  0.16160927 -0.8794039     -1.1484884 -0.9951548
## [259,] -0.9510367  0.89239852 -0.8794039     -1.1484884  1.0016168
## [260,] -0.9510367 -0.56917998  1.1334539     -1.1484884 -0.9951548
## [261,]  1.0480813 -0.44738177  1.1334539      0.8678918  1.0016168
## [262,] -0.9510367 -2.88334594 -0.8794039     -1.1484884 -0.9951548
## [263,]  1.0480813  0.52700390  1.1334539      0.8678918 -0.9951548
## [264,]  1.0480813  1.01419673  1.1334539      0.8678918 -0.9951548
## [265,] -0.9510367  0.89239852 -0.8794039     -1.1484884 -0.9951548
## [266,]  1.0480813 -0.32558356 -0.8794039      0.8678918  1.0016168
## [267,]  1.0480813 -0.93457460 -0.8794039     -1.1484884  1.0016168
## [268,] -0.9510367 -0.32558356 -0.8794039      0.8678918  1.0016168
## [269,]  1.0480813 -0.93457460 -0.8794039      0.8678918  1.0016168
## [270,] -0.9510367 -0.93457460  1.1334539     -1.1484884 -0.9951548
## [271,]  1.0480813  0.89239852 -0.8794039     -1.1484884 -0.9951548
## [272,] -0.9510367  0.03981106 -0.8794039     -1.1484884 -0.9951548
## [273,] -0.9510367  0.16160927 -0.8794039     -1.1484884 -0.9951548
## [274,]  1.0480813 -0.44738177  1.1334539      0.8678918  1.0016168
## [275,] -0.9510367 -0.81277639 -0.8794039     -1.1484884 -0.9951548
## [276,] -0.9510367  0.16160927 -0.8794039      0.8678918  1.0016168
## [277,]  1.0480813 -0.08198714 -0.8794039      0.8678918  1.0016168
## [278,]  1.0480813  2.96296807  1.1334539     -1.1484884 -0.9951548
## [279,]  1.0480813  1.74498598 -0.8794039      0.8678918  1.0016168
## [280,]  1.0480813 -0.44738177  1.1334539      0.8678918  1.0016168
## [281,]  1.0480813 -0.44738177 -0.8794039     -1.1484884 -0.9951548
## [282,] -0.9510367 -0.93457460 -0.8794039     -1.1484884 -0.9951548
## [283,] -0.9510367 -2.03075848  1.1334539      0.8678918  1.0016168
## [284,] -0.9510367 -0.32558356  1.1334539      0.8678918  1.0016168
## [285,] -0.9510367 -0.56917998 -0.8794039      0.8678918  1.0016168
## [286,]  1.0480813 -0.56917998 -0.8794039      0.8678918  1.0016168
## [287,]  1.0480813  0.03981106  1.1334539     -1.1484884 -0.9951548
## [288,]  1.0480813 -1.42176744 -0.8794039      0.8678918  1.0016168
## [289,]  1.0480813 -0.20378535  1.1334539      0.8678918  1.0016168
## [290,]  1.0480813 -0.20378535 -0.8794039     -1.1484884 -0.9951548
## [291,] -0.9510367  1.62318777 -0.8794039     -1.1484884 -0.9951548
## [292,] -0.9510367  1.01419673 -0.8794039      0.8678918  1.0016168
## [293,] -0.9510367  0.77060032  1.1334539     -1.1484884  1.0016168
## [294,]  1.0480813 -0.81277639 -0.8794039      0.8678918  1.0016168
## [295,] -0.9510367  0.52700390  1.1334539     -1.1484884 -0.9951548
## [296,]  1.0480813 -1.05637281 -0.8794039      0.8678918  1.0016168
## [297,] -0.9510367  0.03981106  1.1334539      0.8678918 -0.9951548
## [298,]  1.0480813 -1.90896027 -0.8794039      0.8678918 -0.9951548
## [299,] -0.9510367 -0.08198714 -0.8794039     -1.1484884  1.0016168
## [300,] -0.9510367  0.28340748 -0.8794039      0.8678918  1.0016168
## [301,]  1.0480813  0.03981106 -0.8794039      0.8678918  1.0016168
## [302,] -0.9510367  0.16160927  1.1334539      0.8678918  1.0016168
## [303,]  1.0480813  0.28340748 -0.8794039      0.8678918  1.0016168
## [304,] -0.9510367 -1.42176744  1.1334539      0.8678918 -0.9951548
## [305,]  1.0480813 -0.81277639  1.1334539     -1.1484884 -0.9951548
## [306,] -0.9510367  0.89239852 -0.8794039     -1.1484884 -0.9951548
## [307,] -0.9510367 -0.56917998 -0.8794039     -1.1484884 -0.9951548
## [308,] -0.9510367  0.52700390 -0.8794039     -1.1484884  1.0016168
## [309,] -0.9510367 -0.08198714  1.1334539     -1.1484884 -0.9951548
##        PEER_PRESSURE CHRONIC_DISEASE   FATIGUE    ALLERGY   WHEEZING
##   [1,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
##   [2,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
##   [3,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
##   [4,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
##   [5,]    -1.0016168      -1.0081211 -1.432739 -1.1186650  0.8910297
##   [6,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
##   [7,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
##   [8,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
##   [9,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
##  [10,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
##  [11,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
##  [12,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
##  [13,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
##  [14,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
##  [15,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
##  [16,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [17,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
##  [18,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
##  [19,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
##  [20,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
##  [21,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
##  [22,]     0.9951548      -1.0081211 -1.432739  0.8910297  0.8910297
##  [23,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
##  [24,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
##  [25,]     0.9951548       0.9887342 -1.432739  0.8910297  0.8910297
##  [26,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
##  [27,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
##  [28,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
##  [29,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
##  [30,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
##  [31,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
##  [32,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
##  [33,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
##  [34,]    -1.0016168       0.9887342 -1.432739 -1.1186650 -1.1186650
##  [35,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
##  [36,]    -1.0016168       0.9887342 -1.432739 -1.1186650 -1.1186650
##  [37,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
##  [38,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
##  [39,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
##  [40,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
##  [41,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
##  [42,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
##  [43,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
##  [44,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
##  [45,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
##  [46,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
##  [47,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
##  [48,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
##  [49,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [50,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
##  [51,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [52,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
##  [53,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
##  [54,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [55,]     0.9951548       0.9887342  0.695705  0.8910297 -1.1186650
##  [56,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
##  [57,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
##  [58,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
##  [59,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
##  [60,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
##  [61,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [62,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
##  [63,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
##  [64,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
##  [65,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
##  [66,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
##  [67,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
##  [68,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
##  [69,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
##  [70,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
##  [71,]     0.9951548      -1.0081211 -1.432739  0.8910297 -1.1186650
##  [72,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
##  [73,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
##  [74,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
##  [75,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
##  [76,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
##  [77,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [78,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
##  [79,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
##  [80,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
##  [81,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
##  [82,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
##  [83,]     0.9951548       0.9887342 -1.432739  0.8910297  0.8910297
##  [84,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
##  [85,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
##  [86,]    -1.0016168      -1.0081211 -1.432739 -1.1186650  0.8910297
##  [87,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
##  [88,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
##  [89,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
##  [90,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
##  [91,]     0.9951548      -1.0081211 -1.432739 -1.1186650  0.8910297
##  [92,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
##  [93,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
##  [94,]     0.9951548       0.9887342 -1.432739  0.8910297  0.8910297
##  [95,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
##  [96,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
##  [97,]    -1.0016168      -1.0081211 -1.432739  0.8910297 -1.1186650
##  [98,]     0.9951548      -1.0081211 -1.432739 -1.1186650 -1.1186650
##  [99,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [100,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [101,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [102,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [103,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [104,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [105,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [106,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [107,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [108,]     0.9951548       0.9887342 -1.432739  0.8910297  0.8910297
## [109,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
## [110,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [111,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [112,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [113,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [114,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [115,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [116,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [117,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [118,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [119,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [120,]     0.9951548      -1.0081211 -1.432739  0.8910297 -1.1186650
## [121,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [122,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [123,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [124,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [125,]    -1.0016168      -1.0081211 -1.432739  0.8910297 -1.1186650
## [126,]     0.9951548       0.9887342  0.695705  0.8910297 -1.1186650
## [127,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [128,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [129,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [130,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [131,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [132,]     0.9951548      -1.0081211 -1.432739  0.8910297  0.8910297
## [133,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [134,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [135,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [136,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [137,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [138,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [139,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
## [140,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [141,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [142,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [143,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [144,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [145,]     0.9951548      -1.0081211 -1.432739  0.8910297 -1.1186650
## [146,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [147,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [148,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [149,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [150,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [151,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [152,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [153,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [154,]     0.9951548      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [155,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [156,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [157,]    -1.0016168       0.9887342 -1.432739 -1.1186650 -1.1186650
## [158,]     0.9951548      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [159,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [160,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [161,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [162,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [163,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [164,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [165,]     0.9951548       0.9887342  0.695705  0.8910297 -1.1186650
## [166,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [167,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [168,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
## [169,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [170,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [171,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [172,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [173,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [174,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [175,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [176,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [177,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [178,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [179,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [180,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [181,]     0.9951548      -1.0081211 -1.432739  0.8910297 -1.1186650
## [182,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [183,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [184,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [185,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [186,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [187,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [188,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
## [189,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [190,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [191,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [192,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [193,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [194,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [195,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [196,]    -1.0016168      -1.0081211 -1.432739 -1.1186650  0.8910297
## [197,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
## [198,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [199,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
## [200,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [201,]     0.9951548      -1.0081211 -1.432739 -1.1186650  0.8910297
## [202,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [203,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [204,]     0.9951548       0.9887342 -1.432739  0.8910297  0.8910297
## [205,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [206,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [207,]    -1.0016168      -1.0081211 -1.432739  0.8910297 -1.1186650
## [208,]     0.9951548      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [209,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [210,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [211,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [212,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [213,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [214,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [215,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [216,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [217,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [218,]     0.9951548       0.9887342 -1.432739  0.8910297  0.8910297
## [219,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
## [220,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [221,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [222,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [223,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [224,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [225,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [226,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [227,]     0.9951548       0.9887342  0.695705  0.8910297 -1.1186650
## [228,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [229,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [230,]    -1.0016168       0.9887342 -1.432739  0.8910297 -1.1186650
## [231,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [232,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [233,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [234,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [235,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [236,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [237,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [238,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [239,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [240,]     0.9951548      -1.0081211 -1.432739  0.8910297  0.8910297
## [241,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
## [242,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [243,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [244,]    -1.0016168       0.9887342  0.695705 -1.1186650  0.8910297
## [245,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [246,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [247,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
## [248,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [249,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [250,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
## [251,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [252,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [253,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
## [254,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [255,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [256,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [257,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [258,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [259,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [260,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [261,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [262,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
## [263,]    -1.0016168      -1.0081211 -1.432739 -1.1186650  0.8910297
## [264,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [265,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [266,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [267,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
## [268,]     0.9951548       0.9887342 -1.432739  0.8910297 -1.1186650
## [269,]     0.9951548       0.9887342  0.695705 -1.1186650  0.8910297
## [270,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [271,]    -1.0016168      -1.0081211  0.695705 -1.1186650 -1.1186650
## [272,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [273,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [274,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [275,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [276,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [277,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [278,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [279,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [280,]     0.9951548      -1.0081211 -1.432739  0.8910297  0.8910297
## [281,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [282,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [283,]    -1.0016168      -1.0081211 -1.432739 -1.1186650 -1.1186650
## [284,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [285,]     0.9951548       0.9887342 -1.432739 -1.1186650 -1.1186650
## [286,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [287,]    -1.0016168       0.9887342  0.695705 -1.1186650 -1.1186650
## [288,]     0.9951548      -1.0081211  0.695705 -1.1186650 -1.1186650
## [289,]     0.9951548      -1.0081211 -1.432739  0.8910297  0.8910297
## [290,]    -1.0016168       0.9887342  0.695705  0.8910297 -1.1186650
## [291,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [292,]    -1.0016168       0.9887342 -1.432739  0.8910297  0.8910297
## [293,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [294,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [295,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [296,]    -1.0016168       0.9887342 -1.432739 -1.1186650  0.8910297
## [297,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [298,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [299,]    -1.0016168      -1.0081211  0.695705 -1.1186650  0.8910297
## [300,]     0.9951548      -1.0081211  0.695705  0.8910297 -1.1186650
## [301,]     0.9951548       0.9887342  0.695705  0.8910297  0.8910297
## [302,]     0.9951548      -1.0081211 -1.432739  0.8910297 -1.1186650
## [303,]     0.9951548      -1.0081211  0.695705 -1.1186650  0.8910297
## [304,]    -1.0016168       0.9887342  0.695705  0.8910297  0.8910297
## [305,]     0.9951548       0.9887342  0.695705 -1.1186650 -1.1186650
## [306,]    -1.0016168      -1.0081211  0.695705  0.8910297  0.8910297
## [307,]    -1.0016168      -1.0081211 -1.432739  0.8910297  0.8910297
## [308,]    -1.0016168      -1.0081211  0.695705  0.8910297 -1.1186650
## [309,]     0.9951548      -1.0081211  0.695705  0.8910297  0.8910297
##        ALCOHOL_CONSUMING  COUGHING SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY
##   [1,]         0.8910297  0.850827           0.7475238             1.0617788
##   [2,]        -1.1186650 -1.171523           0.7475238             1.0617788
##   [3,]        -1.1186650  0.850827           0.7475238            -0.9387678
##   [4,]         0.8910297 -1.171523          -1.3334208             1.0617788
##   [5,]        -1.1186650  0.850827           0.7475238            -0.9387678
##   [6,]        -1.1186650  0.850827           0.7475238            -0.9387678
##   [7,]         0.8910297  0.850827           0.7475238            -0.9387678
##   [8,]        -1.1186650 -1.171523           0.7475238             1.0617788
##   [9,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
##  [10,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [11,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [12,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [13,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [14,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [15,]         0.8910297  0.850827          -1.3334208            -0.9387678
##  [16,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [17,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [18,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [19,]        -1.1186650  0.850827           0.7475238            -0.9387678
##  [20,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [21,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [22,]        -1.1186650  0.850827          -1.3334208             1.0617788
##  [23,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [24,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [25,]         0.8910297  0.850827          -1.3334208             1.0617788
##  [26,]         0.8910297  0.850827           0.7475238             1.0617788
##  [27,]         0.8910297 -1.171523           0.7475238             1.0617788
##  [28,]        -1.1186650  0.850827           0.7475238            -0.9387678
##  [29,]         0.8910297 -1.171523           0.7475238             1.0617788
##  [30,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [31,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [32,]         0.8910297 -1.171523           0.7475238             1.0617788
##  [33,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [34,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [35,]        -1.1186650 -1.171523          -1.3334208             1.0617788
##  [36,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [37,]        -1.1186650  0.850827           0.7475238            -0.9387678
##  [38,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [39,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [40,]         0.8910297  0.850827          -1.3334208            -0.9387678
##  [41,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [42,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [43,]         0.8910297 -1.171523          -1.3334208            -0.9387678
##  [44,]         0.8910297 -1.171523           0.7475238            -0.9387678
##  [45,]         0.8910297  0.850827          -1.3334208             1.0617788
##  [46,]         0.8910297  0.850827           0.7475238             1.0617788
##  [47,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [48,]         0.8910297  0.850827          -1.3334208             1.0617788
##  [49,]         0.8910297 -1.171523           0.7475238             1.0617788
##  [50,]         0.8910297 -1.171523          -1.3334208            -0.9387678
##  [51,]         0.8910297 -1.171523          -1.3334208            -0.9387678
##  [52,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [53,]         0.8910297  0.850827          -1.3334208             1.0617788
##  [54,]         0.8910297  0.850827           0.7475238             1.0617788
##  [55,]         0.8910297  0.850827          -1.3334208            -0.9387678
##  [56,]         0.8910297  0.850827          -1.3334208             1.0617788
##  [57,]        -1.1186650  0.850827           0.7475238            -0.9387678
##  [58,]         0.8910297  0.850827           0.7475238             1.0617788
##  [59,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [60,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [61,]         0.8910297  0.850827          -1.3334208             1.0617788
##  [62,]        -1.1186650  0.850827          -1.3334208            -0.9387678
##  [63,]         0.8910297  0.850827          -1.3334208            -0.9387678
##  [64,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [65,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [66,]        -1.1186650  0.850827          -1.3334208             1.0617788
##  [67,]        -1.1186650  0.850827           0.7475238            -0.9387678
##  [68,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [69,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [70,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [71,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [72,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [73,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [74,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [75,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [76,]         0.8910297  0.850827          -1.3334208            -0.9387678
##  [77,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [78,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [79,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [80,]        -1.1186650  0.850827           0.7475238             1.0617788
##  [81,]        -1.1186650 -1.171523           0.7475238            -0.9387678
##  [82,]        -1.1186650 -1.171523           0.7475238             1.0617788
##  [83,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [84,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [85,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [86,]         0.8910297  0.850827           0.7475238             1.0617788
##  [87,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [88,]        -1.1186650 -1.171523          -1.3334208             1.0617788
##  [89,]         0.8910297 -1.171523          -1.3334208            -0.9387678
##  [90,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [91,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [92,]        -1.1186650  0.850827           0.7475238            -0.9387678
##  [93,]         0.8910297 -1.171523          -1.3334208             1.0617788
##  [94,]         0.8910297  0.850827           0.7475238             1.0617788
##  [95,]         0.8910297  0.850827           0.7475238             1.0617788
##  [96,]        -1.1186650 -1.171523          -1.3334208             1.0617788
##  [97,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [98,]         0.8910297  0.850827           0.7475238            -0.9387678
##  [99,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [100,]         0.8910297  0.850827           0.7475238            -0.9387678
## [101,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [102,]        -1.1186650  0.850827           0.7475238             1.0617788
## [103,]         0.8910297  0.850827           0.7475238            -0.9387678
## [104,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [105,]        -1.1186650  0.850827           0.7475238             1.0617788
## [106,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [107,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [108,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [109,]         0.8910297  0.850827           0.7475238            -0.9387678
## [110,]         0.8910297 -1.171523           0.7475238            -0.9387678
## [111,]         0.8910297  0.850827           0.7475238             1.0617788
## [112,]         0.8910297 -1.171523           0.7475238             1.0617788
## [113,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [114,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [115,]         0.8910297  0.850827           0.7475238            -0.9387678
## [116,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [117,]         0.8910297  0.850827           0.7475238            -0.9387678
## [118,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [119,]        -1.1186650  0.850827           0.7475238             1.0617788
## [120,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [121,]        -1.1186650  0.850827           0.7475238             1.0617788
## [122,]         0.8910297  0.850827           0.7475238            -0.9387678
## [123,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [124,]         0.8910297  0.850827           0.7475238            -0.9387678
## [125,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [126,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [127,]         0.8910297  0.850827           0.7475238            -0.9387678
## [128,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [129,]        -1.1186650  0.850827           0.7475238             1.0617788
## [130,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [131,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [132,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [133,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [134,]         0.8910297  0.850827           0.7475238            -0.9387678
## [135,]         0.8910297  0.850827          -1.3334208             1.0617788
## [136,]         0.8910297  0.850827           0.7475238             1.0617788
## [137,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [138,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [139,]         0.8910297 -1.171523           0.7475238             1.0617788
## [140,]         0.8910297  0.850827           0.7475238            -0.9387678
## [141,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [142,]         0.8910297  0.850827           0.7475238            -0.9387678
## [143,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [144,]        -1.1186650  0.850827           0.7475238             1.0617788
## [145,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [146,]        -1.1186650  0.850827           0.7475238             1.0617788
## [147,]         0.8910297  0.850827           0.7475238            -0.9387678
## [148,]         0.8910297  0.850827           0.7475238             1.0617788
## [149,]         0.8910297  0.850827           0.7475238            -0.9387678
## [150,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [151,]         0.8910297  0.850827           0.7475238            -0.9387678
## [152,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [153,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [154,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [155,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [156,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [157,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [158,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [159,]         0.8910297 -1.171523           0.7475238             1.0617788
## [160,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [161,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [162,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [163,]         0.8910297  0.850827          -1.3334208             1.0617788
## [164,]         0.8910297  0.850827           0.7475238             1.0617788
## [165,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [166,]         0.8910297  0.850827          -1.3334208             1.0617788
## [167,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [168,]         0.8910297  0.850827           0.7475238             1.0617788
## [169,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [170,]         0.8910297  0.850827           0.7475238            -0.9387678
## [171,]         0.8910297  0.850827          -1.3334208             1.0617788
## [172,]        -1.1186650  0.850827          -1.3334208            -0.9387678
## [173,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [174,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [175,]         0.8910297  0.850827           0.7475238            -0.9387678
## [176,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [177,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [178,]         0.8910297  0.850827           0.7475238            -0.9387678
## [179,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [180,]        -1.1186650  0.850827           0.7475238             1.0617788
## [181,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [182,]        -1.1186650  0.850827           0.7475238             1.0617788
## [183,]         0.8910297  0.850827           0.7475238            -0.9387678
## [184,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [185,]         0.8910297  0.850827           0.7475238            -0.9387678
## [186,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [187,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [188,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [189,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [190,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [191,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [192,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [193,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [194,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [195,]         0.8910297  0.850827           0.7475238            -0.9387678
## [196,]         0.8910297  0.850827           0.7475238             1.0617788
## [197,]         0.8910297  0.850827           0.7475238            -0.9387678
## [198,]        -1.1186650 -1.171523          -1.3334208             1.0617788
## [199,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [200,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [201,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [202,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [203,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [204,]         0.8910297  0.850827           0.7475238             1.0617788
## [205,]         0.8910297  0.850827           0.7475238             1.0617788
## [206,]        -1.1186650 -1.171523          -1.3334208             1.0617788
## [207,]         0.8910297  0.850827           0.7475238            -0.9387678
## [208,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [209,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [210,]         0.8910297  0.850827           0.7475238            -0.9387678
## [211,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [212,]        -1.1186650  0.850827           0.7475238             1.0617788
## [213,]         0.8910297  0.850827           0.7475238            -0.9387678
## [214,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [215,]        -1.1186650  0.850827           0.7475238             1.0617788
## [216,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [217,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [218,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [219,]         0.8910297  0.850827           0.7475238            -0.9387678
## [220,]         0.8910297  0.850827           0.7475238            -0.9387678
## [221,]         0.8910297 -1.171523           0.7475238             1.0617788
## [222,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [223,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [224,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [225,]         0.8910297  0.850827          -1.3334208             1.0617788
## [226,]         0.8910297  0.850827           0.7475238             1.0617788
## [227,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [228,]         0.8910297  0.850827          -1.3334208             1.0617788
## [229,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [230,]         0.8910297  0.850827           0.7475238             1.0617788
## [231,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [232,]         0.8910297  0.850827           0.7475238            -0.9387678
## [233,]         0.8910297  0.850827          -1.3334208             1.0617788
## [234,]        -1.1186650  0.850827          -1.3334208            -0.9387678
## [235,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [236,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [237,]         0.8910297  0.850827           0.7475238            -0.9387678
## [238,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [239,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [240,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [241,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [242,]         0.8910297  0.850827           0.7475238            -0.9387678
## [243,]        -1.1186650 -1.171523          -1.3334208             1.0617788
## [244,]         0.8910297  0.850827           0.7475238             1.0617788
## [245,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [246,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [247,]         0.8910297 -1.171523           0.7475238             1.0617788
## [248,]         0.8910297  0.850827           0.7475238            -0.9387678
## [249,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [250,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [251,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [252,]        -1.1186650  0.850827           0.7475238             1.0617788
## [253,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [254,]        -1.1186650  0.850827           0.7475238             1.0617788
## [255,]         0.8910297  0.850827           0.7475238            -0.9387678
## [256,]         0.8910297  0.850827           0.7475238             1.0617788
## [257,]         0.8910297  0.850827           0.7475238            -0.9387678
## [258,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [259,]         0.8910297  0.850827           0.7475238            -0.9387678
## [260,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [261,]         0.8910297 -1.171523          -1.3334208            -0.9387678
## [262,]         0.8910297 -1.171523           0.7475238            -0.9387678
## [263,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [264,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [265,]         0.8910297  0.850827           0.7475238            -0.9387678
## [266,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [267,]        -1.1186650 -1.171523          -1.3334208            -0.9387678
## [268,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [269,]        -1.1186650  0.850827           0.7475238             1.0617788
## [270,]         0.8910297  0.850827           0.7475238            -0.9387678
## [271,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [272,]         0.8910297  0.850827           0.7475238            -0.9387678
## [273,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [274,]        -1.1186650  0.850827           0.7475238             1.0617788
## [275,]         0.8910297  0.850827           0.7475238            -0.9387678
## [276,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [277,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [278,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [279,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [280,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [281,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [282,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [283,]        -1.1186650 -1.171523          -1.3334208             1.0617788
## [284,]         0.8910297  0.850827           0.7475238             1.0617788
## [285,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [286,]        -1.1186650  0.850827           0.7475238             1.0617788
## [287,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [288,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [289,]        -1.1186650  0.850827          -1.3334208             1.0617788
## [290,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [291,]         0.8910297  0.850827           0.7475238            -0.9387678
## [292,]         0.8910297  0.850827          -1.3334208             1.0617788
## [293,]         0.8910297  0.850827           0.7475238             1.0617788
## [294,]        -1.1186650 -1.171523           0.7475238            -0.9387678
## [295,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [296,]         0.8910297 -1.171523           0.7475238             1.0617788
## [297,]         0.8910297  0.850827           0.7475238            -0.9387678
## [298,]        -1.1186650  0.850827           0.7475238            -0.9387678
## [299,]         0.8910297  0.850827           0.7475238            -0.9387678
## [300,]        -1.1186650 -1.171523           0.7475238             1.0617788
## [301,]        -1.1186650  0.850827           0.7475238             1.0617788
## [302,]         0.8910297 -1.171523          -1.3334208             1.0617788
## [303,]        -1.1186650  0.850827           0.7475238             1.0617788
## [304,]         0.8910297  0.850827           0.7475238            -0.9387678
## [305,]         0.8910297  0.850827           0.7475238             1.0617788
## [306,]         0.8910297  0.850827           0.7475238            -0.9387678
## [307,]         0.8910297  0.850827          -1.3334208            -0.9387678
## [308,]         0.8910297  0.850827           0.7475238            -0.9387678
## [309,]         0.8910297 -1.171523          -1.3334208             1.0617788
##        CHEST_PAIN       WEIGHT  HEIGHT_INCH
##   [1,]  0.8910297 -1.139073343 -1.116375616
##   [2,]  0.8910297  0.808283891  1.857563907
##   [3,]  0.8910297  2.179162116  0.759454418
##   [4,]  0.8910297  1.293001354  0.146112791
##   [5,] -1.1186650  1.455596085 -0.076360652
##   [6,] -1.1186650 -0.284541347  0.395799397
##   [7,]  0.8910297  1.223320266  0.968702627
##   [8,] -1.1186650  0.806211776  1.079049538
##   [9,] -1.1186650 -1.190478376 -0.016777055
##  [10,]  0.8910297 -0.502958860 -0.598028422
##  [11,] -1.1186650  0.059363459 -0.750915032
##  [12,]  0.8910297 -1.043714604 -0.161699470
##  [13,] -1.1186650 -0.093218811  0.190670779
##  [14,]  0.8910297 -0.354214146 -0.424632063
##  [15,]  0.8910297 -0.882620085  0.178836036
##  [16,] -1.1186650  1.099225434  1.637778056
##  [17,]  0.8910297  0.229334920 -0.764762874
##  [18,]  0.8910297  1.345873444  0.370599334
##  [19,] -1.1186650  0.925582185  1.709756742
##  [20,] -1.1186650 -0.222999527 -0.417046621
##  [21,] -1.1186650  1.205582961 -0.052504384
##  [22,] -1.1186650  1.392777843  0.489693889
##  [23,] -1.1186650 -2.389850946 -2.310828522
##  [24,]  0.8910297  0.229368074  0.252615097
##  [25,]  0.8910297  1.252777455 -0.159255733
##  [26,]  0.8910297  0.247743591 -0.376857268
##  [27,]  0.8910297  1.300303488  1.508457163
##  [28,]  0.8910297  0.399074304 -0.228624653
##  [29,]  0.8910297 -1.525323894 -0.726882359
##  [30,] -1.1186650 -1.064502064 -1.293990144
##  [31,] -1.1186650 -1.942299769  0.824081140
##  [32,]  0.8910297 -0.495797630 -1.100867485
##  [33,] -1.1186650 -0.078473640 -0.061578897
##  [34,]  0.8910297  0.786336048  1.380148008
##  [35,]  0.8910297  1.107845433  2.007835563
##  [36,] -1.1186650  0.166873082  0.659520628
##  [37,]  0.8910297  1.248575206 -0.586966751
##  [38,] -1.1186650 -0.456153923 -0.143228763
##  [39,]  0.8910297  0.382298460 -0.066398922
##  [40,]  0.8910297 -1.659671552 -2.018098942
##  [41,]  0.8910297 -0.196899165  0.331873110
##  [42,] -1.1186650 -0.155514881 -1.427544772
##  [43,] -1.1186650  1.072171899  0.894041538
##  [44,]  0.8910297  0.881412979  0.016771145
##  [45,] -1.1186650 -1.681354165 -1.013868379
##  [46,]  0.8910297  0.168132928  0.382646801
##  [47,]  0.8910297  1.570523880 -0.546912296
##  [48,]  0.8910297 -0.821915399 -0.122604869
##  [49,]  0.8910297  1.399599246  0.978628038
##  [50,] -1.1186650  0.679414906  0.598318250
##  [51,]  0.8910297  1.681440059  1.027201847
##  [52,] -1.1186650 -0.033724241 -0.312946545
##  [53,]  0.8910297 -0.103728579  1.211182544
##  [54,]  0.8910297 -0.913967043  0.606240939
##  [55,] -1.1186650 -0.269058502 -1.323781942
##  [56,] -1.1186650  1.753607685  1.167122643
##  [57,]  0.8910297  2.417190127  1.282149491
##  [58,]  0.8910297  0.110967415 -0.721823668
##  [59,]  0.8910297 -0.610468482 -0.814996972
##  [60,]  0.8910297  0.586774783 -0.206490935
##  [61,]  0.8910297  0.165530351 -0.742359359
##  [62,] -1.1186650  0.895975804  0.552354207
##  [63,] -1.1186650  0.250727437  0.191225937
##  [64,] -1.1186650  0.173114292 -0.478596621
##  [65,]  0.8910297  0.711242595  1.489555818
##  [66,]  0.8910297 -1.419322772  0.147622616
##  [67,]  0.8910297  1.304025007  0.583256323
##  [68,] -1.1186650  0.498436370 -0.105820392
##  [69,]  0.8910297 -1.923576137 -0.373204633
##  [70,] -1.1186650 -0.166223572 -0.294366881
##  [71,]  0.8910297  0.213702884 -1.382530206
##  [72,] -1.1186650  0.603575492  1.508680264
##  [73,]  0.8910297  1.132329546  1.032198277
##  [74,] -1.1186650 -1.980965438 -1.893717407
##  [75,]  0.8910297  0.148033411  0.160951618
##  [76,] -1.1186650 -0.533468683 -0.818680736
##  [77,]  0.8910297  0.983692583  0.221941271
##  [78,]  0.8910297  0.515709522 -1.275353408
##  [79,]  0.8910297 -0.921020523  0.925862000
##  [80,]  0.8910297 -0.349058724 -0.108668824
##  [81,] -1.1186650  0.653961044  0.365483571
##  [82,] -1.1186650 -0.400894756 -0.597151582
##  [83,]  0.8910297  2.373924363  1.098116911
##  [84,] -1.1186650  0.182878099 -0.859461567
##  [85,]  0.8910297  0.196098193  0.657367441
##  [86,] -1.1186650  1.055777324  0.622516952
##  [87,]  0.8910297  1.173208234 -0.296063488
##  [88,]  0.8910297  0.402505727  1.119648775
##  [89,] -1.1186650 -0.465163479  1.163039372
##  [90,]  0.8910297  0.395966132  0.150761599
##  [91,]  0.8910297  0.813306699  0.100828428
##  [92,]  0.8910297  1.222897555  1.197262064
##  [93,]  0.8910297  1.150025409  1.843197225
##  [94,] -1.1186650 -1.209624720  0.658815005
##  [95,]  0.8910297  0.557118671  1.104130268
##  [96,]  0.8910297  0.419787167  1.360421708
##  [97,]  0.8910297 -0.555897257 -0.855331600
##  [98,] -1.1186650 -0.301549268 -2.339561886
##  [99,] -1.1186650  0.116686453 -0.605940733
## [100,]  0.8910297 -0.933237713  0.494155914
## [101,] -1.1186650 -2.042498969 -1.587985694
## [102,]  0.8910297  0.299844854 -0.437001211
## [103,]  0.8910297  0.617392356  0.214086032
## [104,]  0.8910297 -2.328564411 -1.205917039
## [105,]  0.8910297 -1.009160012 -0.093119186
## [106,] -1.1186650 -0.268851291  0.044731438
## [107,] -1.1186650 -0.305627190 -0.141672242
## [108,]  0.8910297 -0.021399300 -0.840721063
## [109,] -1.1186650  0.139380258  0.779336370
## [110,]  0.8910297  0.038020673 -2.126593593
## [111,]  0.8910297 -0.387832142 -0.110106011
## [112,]  0.8910297  0.072193996  1.097862679
## [113,]  0.8910297  0.406707977  1.167926845
## [114,]  0.8910297 -1.229997756 -1.032027782
## [115,] -1.1186650 -0.389257758  1.075044092
## [116,] -1.1186650  0.150793468  0.350893787
## [117,]  0.8910297  0.492651024  0.453043025
## [118,] -1.1186650  0.773132530  0.947990530
## [119,] -1.1186650 -0.894746103 -1.286513659
## [120,]  0.8910297  0.842830195  0.461951509
## [121,] -1.1186650 -0.568172467 -1.107560523
## [122,]  0.8910297 -1.469534266 -0.373692343
## [123,] -1.1186650  0.127237663  0.770593914
## [124,] -1.1186650  0.709153903  0.523496321
## [125,]  0.8910297 -1.647711303  0.003379882
## [126,] -1.1186650 -0.285245866 -1.198482060
## [127,]  0.8910297 -1.427362579 -0.746567152
## [128,]  0.8910297 -0.615557597 -0.003577763
## [129,] -1.1186650  1.119341528  0.497652896
## [130,] -1.1186650  0.600807146  1.196452674
## [131,] -1.1186650  0.484486891  0.171862825
## [132,] -1.1186650  0.328506351  1.710420857
## [133,] -1.1186650 -0.925960445  0.603143463
## [134,]  0.8910297 -0.243786986 -1.835685142
## [135,]  0.8910297  0.116645010  1.639983126
## [136,] -1.1186650  0.764960108  0.147191979
## [137,]  0.8910297 -0.837804378 -1.046902927
## [138,]  0.8910297  0.007353369 -0.258426828
## [139,]  0.8910297  2.043596055  3.095443729
## [140,] -1.1186650  0.303922777  1.061808481
## [141,] -1.1186650  0.785034760  0.821652968
## [142,]  0.8910297 -1.105389040 -1.427129700
## [143,] -1.1186650 -0.116592270  0.038240748
## [144,]  0.8910297  0.070387112  0.209307515
## [145,]  0.8910297 -1.622796191 -1.427233468
## [146,] -1.1186650 -0.851770434  0.169714827
## [147,]  0.8910297  0.588880052  0.328770446
## [148,] -1.1186650 -1.147560727 -1.783894524
## [149,]  0.8910297  0.333313658  0.402383478
## [150,]  0.8910297  0.913530764  0.496267593
## [151,]  0.8910297 -0.110384213  0.832802842
## [152,] -1.1186650  0.972279372 -0.277758810
## [153,] -1.1186650 -0.490426707 -0.757390156
## [154,]  0.8910297  1.112188587 -0.997633872
## [155,] -1.1186650  0.829203966  2.339633802
## [156,]  0.8910297 -1.709203392 -1.976036576
## [157,]  0.8910297  2.670609809  1.580456602
## [158,]  0.8910297 -1.487661130 -0.225044657
## [159,]  0.8910297  0.997965312  2.116952823
## [160,] -1.1186650 -0.896959121 -1.361205878
## [161,]  0.8910297  1.620959162 -0.446148362
## [162,] -1.1186650 -1.397341775 -1.838512821
## [163,]  0.8910297  1.020683982  0.744558519
## [164,]  0.8910297 -0.566539641  0.230481379
## [165,] -1.1186650  0.130254663 -1.361854428
## [166,] -1.1186650  0.042057154 -0.414078856
## [167,]  0.8910297 -0.953569307  0.238507835
## [168,]  0.8910297 -0.160620573 -0.852550617
## [169,]  0.8910297  0.017879714 -0.388292503
## [170,]  0.8910297 -1.281750904 -1.008327167
## [171,]  0.8910297 -0.342021821  0.777712401
## [172,] -1.1186650 -0.209447894  0.020569054
## [173,] -1.1186650 -0.173235610 -0.090099537
## [174,] -1.1186650 -0.598301022 -1.378218645
## [175,]  0.8910297  1.041272518  3.060458341
## [176,]  0.8910297 -1.815909034 -0.582068901
## [177,]  0.8910297 -0.306091344 -0.540048042
## [178,] -1.1186650 -0.650070746 -1.141087969
## [179,]  0.8910297 -0.434438156 -1.012856641
## [180,] -1.1186650 -0.620522384 -0.700966296
## [181,]  0.8910297  0.686990559 -0.426510264
## [182,] -1.1186650 -0.870900201 -1.068901747
## [183,]  0.8910297 -1.455642806 -0.598905262
## [184,] -1.1186650 -0.208179759  0.415479002
## [185,]  0.8910297  1.195951769 -0.886347861
## [186,] -1.1186650  0.200142962 -1.024867789
## [187,] -1.1186650  0.093984359  0.336589366
## [188,] -1.1186650 -0.481640939 -0.696032127
## [189,] -1.1186650  0.075525958 -0.502883526
## [190,] -1.1186650 -2.094169232  0.075317061
## [191,] -1.1186650  1.513250617  1.170121539
## [192,] -1.1186650 -1.308174516 -1.252218329
## [193,] -1.1186650  0.507843773 -0.246934520
## [194,] -1.1186650  1.624796719 -0.272461453
## [195,]  0.8910297  1.562707861  0.895826347
## [196,] -1.1186650 -0.488379458 -1.108759043
## [197,]  0.8910297 -0.907924755 -0.949169019
## [198,]  0.8910297  0.129840240  0.158186200
## [199,] -1.1186650  0.061037728  0.046199755
## [200,]  0.8910297  0.094547975  1.792828229
## [201,]  0.8910297 -0.433957425 -1.143204837
## [202,]  0.8910297 -1.162090398 -0.778989469
## [203,]  0.8910297  0.685175387  1.078203828
## [204,] -1.1186650  0.161087736  0.802372870
## [205,]  0.8910297 -0.193053319  0.359376823
## [206,]  0.8910297  1.101587646  0.221941271
## [207,]  0.8910297 -0.763896175  0.236224939
## [208,] -1.1186650  1.420502743  0.435381708
## [209,] -1.1186650  1.196432500  1.031772828
## [210,]  0.8910297  2.420729300  1.878426467
## [211,] -1.1186650  0.602895838  0.265985606
## [212,]  0.8910297  0.278667838 -0.633506707
## [213,]  0.8910297 -1.699870586 -0.648994084
## [214,]  0.8910297 -1.217283257  0.001039913
## [215,]  0.8910297  0.783509683  0.499935792
## [216,] -1.1186650  0.373031961 -0.333653453
## [217,] -1.1186650  0.380251211  0.849410913
## [218,]  0.8910297 -0.597538483 -0.134999959
## [219,] -1.1186650 -0.807203382  0.574129925
## [220,]  0.8910297  0.977219295  0.016947551
## [221,]  0.8910297 -1.415965946 -1.087055962
## [222,] -1.1186650  0.283591183 -1.121787118
## [223,]  0.8910297  0.860012174  1.663439887
## [224,] -1.1186650 -1.075542293 -0.054185426
## [225,]  0.8910297 -0.974961824 -1.486832630
## [226,]  0.8910297  0.081186976  0.919625542
## [227,] -1.1186650 -0.392722334  1.035005202
## [228,] -1.1186650 -0.727286045 -0.943923546
## [229,]  0.8910297  0.081120668  0.352113062
## [230,]  0.8910297 -0.727186584  0.551326903
## [231,]  0.8910297 -0.130956172 -0.593177267
## [232,]  0.8910297  1.190821212  0.045992219
## [233,]  0.8910297  1.553822632  0.901533588
## [234,] -1.1186650 -0.884410392  2.016624714
## [235,] -1.1186650  0.746824956  2.496541422
## [236,] -1.1186650  0.513007484 -0.340087070
## [237,]  0.8910297 -0.917796311 -0.272305801
## [238,]  0.8910297 -1.029176645  0.309495536
## [239,]  0.8910297  1.841415636  0.278240609
## [240,] -1.1186650  1.280767586  0.302838818
## [241,] -1.1186650  0.610745011 -2.184158902
## [242,]  0.8910297  1.256300051 -0.119414002
## [243,]  0.8910297  0.995362735  0.797023629
## [244,] -1.1186650  0.639340200 -0.639732789
## [245,]  0.8910297 -0.805529113 -1.402801288
## [246,]  0.8910297 -0.916718812  1.016793915
## [247,]  0.8910297  0.667645292  0.983458439
## [248,] -1.1186650 -0.510633974 -1.316341776
## [249,] -1.1186650 -0.551338604  0.200871175
## [250,] -1.1186650 -3.512283394 -1.035623344
## [251,] -1.1186650  1.011525233  1.122284482
## [252,]  0.8910297  1.391559439 -0.975251111
## [253,]  0.8910297 -0.298441095  0.155560870
## [254,] -1.1186650 -0.929076906 -1.409899021
## [255,]  0.8910297 -0.476667863  0.636484128
## [256,] -1.1186650 -0.504608263 -0.173471952
## [257,]  0.8910297 -0.223803508 -0.336610842
## [258,]  0.8910297 -0.788363711 -0.566446626
## [259,]  0.8910297  0.101485416  0.076697176
## [260,] -1.1186650 -0.827410649 -0.708255999
## [261,] -1.1186650 -0.392846661  1.159474940
## [262,]  0.8910297 -0.227118892 -0.043507697
## [263,] -1.1186650 -1.482008400 -0.680664083
## [264,] -1.1186650 -1.829924821 -2.203423434
## [265,]  0.8910297  0.456911182  0.052202735
## [266,] -1.1186650  0.037133808 -0.515719630
## [267,] -1.1186650 -0.133815691 -0.867534719
## [268,]  0.8910297  0.545929249  1.450217362
## [269,] -1.1186650 -0.364607876  1.438979286
## [270,]  0.8910297  0.292434971  2.767355197
## [271,] -1.1186650 -0.828206341 -2.150475803
## [272,]  0.8910297 -0.073102717 -0.048716851
## [273,]  0.8910297 -2.163982935 -0.080111865
## [274,] -1.1186650 -0.683042243 -0.361100094
## [275,]  0.8910297  0.861180847 -0.611181018
## [276,]  0.8910297 -0.666084052  0.568645786
## [277,] -1.1186650 -0.213119682  0.306911713
## [278,] -1.1186650 -0.148461401 -1.702208340
## [279,] -1.1186650 -0.028718011 -1.448620057
## [280,] -1.1186650 -0.431819003 -0.619363127
## [281,] -1.1186650  0.543699653 -0.485507571
## [282,]  0.8910297  0.055683383  1.209480748
## [283,]  0.8910297 -0.137205672 -0.185913737
## [284,]  0.8910297 -1.982929803 -0.845276479
## [285,]  0.8910297  0.620459086  0.504330368
## [286,] -1.1186650 -2.135072785 -1.208666891
## [287,] -1.1186650  1.587506935  0.034712635
## [288,] -1.1186650  2.367948383  1.038803112
## [289,] -1.1186650  0.993133139  1.147110981
## [290,] -1.1186650 -0.868156721 -0.659625118
## [291,]  0.8910297 -0.507807609  0.763615515
## [292,]  0.8910297 -1.021725319 -0.585773419
## [293,] -1.1186650  0.547470903 -0.121670957
## [294,]  0.8910297 -2.816902273  0.622293851
## [295,]  0.8910297  0.418328398 -0.206132935
## [296,]  0.8910297 -0.691993780 -1.118549556
## [297,] -1.1186650  0.365622078 -0.870248253
## [298,] -1.1186650  0.287437029 -0.282563269
## [299,]  0.8910297  0.202919597 -1.552222047
## [300,] -1.1186650  1.360063289  0.685908835
## [301,]  0.8910297  0.994227216  0.592725154
## [302,]  0.8910297  0.349559041  0.886720704
## [303,] -1.1186650 -0.201590433  0.592548749
## [304,]  0.8910297  0.715693498  0.040497702
## [305,] -1.1186650 -0.210243586  0.478191204
## [306,]  0.8910297 -1.284419788 -2.461069047
## [307,]  0.8910297  0.221162498 -1.223983051
## [308,]  0.8910297  0.083632072  0.615356959
## [309,] -1.1186650 -0.447931770  0.961236518
## attr(,"scaled:center")
##                GENDER                   AGE               SMOKING 
##             0.4757282            62.6731392             0.4368932 
##        YELLOW_FINGERS               ANXIETY         PEER_PRESSURE 
##             0.5695793             0.4983819             0.5016181 
##       CHRONIC_DISEASE               FATIGUE               ALLERGY 
##             0.5048544             0.6731392             0.5566343 
##              WHEEZING     ALCOHOL_CONSUMING              COUGHING 
##             0.5566343             0.5566343             0.5792880 
##   SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY            CHEST_PAIN 
##             0.6407767             0.4692557             0.5566343 
##                WEIGHT           HEIGHT_INCH 
##           126.7353818            67.9349857 
## attr(,"scaled:scale")
##                GENDER                   AGE               SMOKING 
##             0.5002206             8.2103014             0.4968061 
##        YELLOW_FINGERS               ANXIETY         PEER_PRESSURE 
##             0.4959382             0.5008084             0.5008084 
##       CHRONIC_DISEASE               FATIGUE               ALLERGY 
##             0.5007874             0.4698268             0.4975880 
##              WHEEZING     ALCOHOL_CONSUMING              COUGHING 
##             0.4975880             0.4975880             0.4944742 
##   SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY            CHEST_PAIN 
##             0.4805510             0.4998634             0.4975880 
##                WEIGHT           HEIGHT_INCH 
##            12.0649666             1.9273761
#as.matrix(scale.emp) %*% fact.load.emp %*% solve(t(fact.load.emp) %*% fact.load.emp + diag(ncol(fact.load.emp)))

Cluster Analysis

library(cluster)
library(readr)
library(factoextra)
library(magrittr)
## 
## Attaching package: 'magrittr'
## The following object is masked from 'package:purrr':
## 
##     set_names
## The following object is masked from 'package:tidyr':
## 
##     extract
library(NbClust)

lung <- read.csv("/Users/batul/Desktop/MVA/LUNGCANCER3.csv")
lung
##     LUNG_CANCER GENDER AGE SMOKING YELLOW_FINGERS ANXIETY PEER_PRESSURE
## 1             1      0  69       1              1       1             0
## 2             1      0  74       0              0       0             0
## 3             0      1  59       1              0       0             1
## 4             0      0  63       0              1       1             0
## 5             0      1  63       1              1       0             0
## 6             1      1  75       1              1       0             0
## 7             1      0  52       0              0       0             0
## 8             1      1  51       0              1       1             1
## 9             0      1  68       0              0       1             0
## 10            1      0  53       0              1       1             1
## 11            1      1  61       0              1       1             1
## 12            1      0  72       1              0       0             0
## 13            0      1  60       0              0       0             0
## 14            1      0  58       0              0       0             0
## 15            0      0  69       0              0       0             0
## 16            1      1  48       1              1       1             1
## 17            1      0  75       0              0       0             0
## 18            1      0  57       0              1       1             1
## 19            1      1  68       0              1       1             1
## 20            0      1  61       1              0       0             0
## 21            1      1  44       0              1       1             1
## 22            1      1  64       1              1       1             1
## 23            0      1  21       0              0       0             0
## 24            1      0  60       0              0       0             0
## 25            1      0  72       0              1       1             1
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##     CHRONIC_DISEASE FATIGUE ALLERGY WHEEZING ALCOHOL_CONSUMING COUGHING
## 1                 0       1       0        1                 1        1
## 2                 1       1       1        0                 0        0
## 3                 0       1       0        1                 0        1
## 4                 0       0       0        0                 1        0
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## 12                1       1       1        1                 1        1
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## 14                0       1       1        1                 1        1
## 15                0       0       1        1                 1        1
## 16                1       1       1        1                 0        1
## 17                1       0       1        1                 1        1
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## 23                1       1       1        0                 0        0
## 24                0       1       1        1                 1        1
## 25                1       0       1        1                 1        1
## 26                0       1       0        1                 1        1
## 27                0       1       1        0                 1        0
## 28                0       1       0        1                 0        1
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## 30                0       1       0        1                 1        1
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## 53                0       1       1        1                 1        1
## 54                1       1       1        1                 1        1
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## 56                1       0       1        1                 1        1
## 57                0       1       0        0                 0        1
## 58                1       0       1        0                 1        1
## 59                1       1       0        1                 0        0
## 60                0       1       1        0                 1        1
## 61                1       1       1        1                 1        1
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## 64                1       0       1        1                 1        0
## 65                0       1       1        1                 1        1
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## 85                1       1       1        0                 1        1
## 86                0       0       0        1                 1        1
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## 89                1       0       1        0                 1        0
## 90                1       1       1        1                 1        0
## 91                0       0       0        1                 1        0
## 92                1       1       1        0                 0        1
## 93                1       1       1        1                 1        0
## 94                1       0       1        1                 1        1
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## 163               0       1       1        1                 1        1
## 164               1       1       1        1                 1        1
## 165               1       1       1        0                 1        1
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## 167               0       1       0        0                 0        1
## 168               1       0       1        0                 1        1
## 169               1       1       0        1                 0        0
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## 171               1       1       1        1                 1        1
## 172               0       0       0        0                 0        1
## 173               0       1       1        1                 1        1
## 174               1       0       1        1                 1        0
## 175               0       1       1        1                 1        1
## 176               1       1       0        1                 0        1
## 177               1       1       1        1                 0        1
## 178               0       1       0        1                 1        1
## 179               0       1       1        0                 0        0
## 180               0       1       0        1                 0        1
## 181               0       0       1        0                 1        0
## 182               0       1       0        1                 0        1
## 183               1       1       1        1                 1        1
## 184               1       1       0        0                 0        0
## 185               0       1       1        1                 1        1
## 186               0       0       1        1                 1        1
## 187               1       1       0        0                 0        0
## 188               0       1       0        0                 0        0
## 189               1       0       0        0                 0        0
## 190               0       1       0        0                 0        0
## 191               1       1       0        0                 0        0
## 192               1       1       0        0                 0        0
## 193               1       0       0        0                 0        0
## 194               1       0       0        0                 0        0
## 195               1       1       1        0                 1        1
## 196               0       0       0        1                 1        1
## 197               1       0       1        0                 1        1
## 198               0       1       0        1                 0        0
## 199               1       0       1        0                 1        0
## 200               1       1       1        1                 1        0
## 201               0       0       0        1                 1        0
## 202               1       1       1        0                 0        1
## 203               1       1       1        1                 1        0
## 204               1       0       1        1                 1        1
## 205               1       1       1        0                 1        1
## 206               0       1       0        0                 0        0
## 207               0       0       1        0                 1        1
## 208               0       0       0        0                 0        1
## 209               0       1       1        0                 0        1
## 210               0       1       1        1                 1        1
## 211               0       0       1        1                 1        1
## 212               1       1       1        1                 0        1
## 213               0       1       1        1                 1        1
## 214               1       0       0        0                 1        0
## 215               0       1       0        0                 0        1
## 216               1       1       0        0                 0        0
## 217               1       1       0        0                 0        0
## 218               1       0       1        1                 1        0
## 219               1       0       1        0                 1        1
## 220               1       1       1        0                 1        1
## 221               1       1       1        1                 1        0
## 222               1       0       0        0                 1        0
## 223               1       1       1        1                 1        0
## 224               1       1       1        1                 0        0
## 225               0       1       1        1                 1        1
## 226               1       1       1        1                 1        1
## 227               1       1       1        0                 1        1
## 228               1       0       1        1                 1        1
## 229               0       1       0        0                 0        1
## 230               1       0       1        0                 1        1
## 231               1       1       0        1                 0        0
## 232               0       1       1        0                 1        1
## 233               1       1       1        1                 1        1
## 234               0       0       0        0                 0        1
## 235               0       1       1        1                 1        1
## 236               1       0       1        1                 1        0
## 237               0       1       1        1                 1        1
## 238               1       1       0        1                 0        1
## 239               1       1       1        1                 0        1
## 240               0       0       1        1                 0        1
## 241               1       0       1        0                 0        0
## 242               0       1       1        1                 1        1
## 243               1       0       1        1                 0        0
## 244               1       1       0        1                 1        1
## 245               0       1       1        0                 0        0
## 246               0       1       0        1                 0        0
## 247               1       0       0        1                 1        0
## 248               0       1       0        1                 1        1
## 249               1       1       1        1                 0        1
## 250               0       1       0        0                 0        0
## 251               0       1       1        0                 0        0
## 252               1       1       1        1                 0        1
## 253               1       0       1        0                 1        0
## 254               0       1       0        1                 0        1
## 255               1       1       1        1                 1        1
## 256               1       1       0        0                 1        1
## 257               0       1       1        1                 1        1
## 258               0       0       1        1                 1        1
## 259               0       1       1        0                 1        1
## 260               0       1       1        1                 1        0
## 261               1       1       0        1                 1        0
## 262               0       1       1        1                 1        0
## 263               0       0       0        1                 0        1
## 264               1       1       1        1                 0        1
## 265               0       1       0        1                 1        1
## 266               0       1       1        0                 0        0
## 267               0       1       0        0                 0        0
## 268               1       0       1        0                 1        0
## 269               1       1       0        1                 0        1
## 270               1       1       1        1                 1        1
## 271               0       1       0        0                 0        0
## 272               0       1       1        1                 1        1
## 273               0       0       1        1                 1        1
## 274               1       1       1        1                 0        1
## 275               1       0       1        1                 1        1
## 276               1       0       0        0                 1        0
## 277               1       1       0        0                 0        1
## 278               1       1       0        0                 0        0
## 279               1       1       0        0                 0        0
## 280               0       0       1        1                 0        1
## 281               1       1       1        0                 0        0
## 282               0       1       1        0                 0        0
## 283               0       0       0        0                 0        0
## 284               0       1       0        1                 1        1
## 285               1       0       0        0                 1        0
## 286               0       1       0        0                 0        1
## 287               1       1       0        0                 0        0
## 288               0       1       0        0                 0        0
## 289               0       0       1        1                 0        1
## 290               1       1       1        0                 0        0
## 291               0       1       1        1                 1        1
## 292               1       0       1        1                 1        1
## 293               0       1       0        1                 1        1
## 294               0       1       1        0                 0        0
## 295               0       1       0        1                 0        1
## 296               1       0       0        1                 1        0
## 297               0       1       0        1                 1        1
## 298               1       1       1        1                 0        1
## 299               0       1       0        1                 1        1
## 300               0       1       1        0                 0        0
## 301               1       1       1        1                 0        1
## 302               0       0       1        0                 1        0
## 303               0       1       0        1                 0        1
## 304               1       1       1        1                 1        1
## 305               1       1       0        0                 1        1
## 306               0       1       1        1                 1        1
## 307               0       0       1        1                 1        1
## 308               0       1       1        0                 1        1
## 309               0       1       1        1                 1        0
##     SHORTNESS_OF_BREATH SWALLOWING_DIFFICULTY CHEST_PAIN    WEIGHT HEIGHT_INCH
## 1                     1                     1          1 112.99250    65.78331
## 2                     1                     1          1 136.48730    71.51521
## 3                     1                     0          1 153.02690    69.39874
## 4                     0                     1          1 142.33540    68.21660
## 5                     1                     0          0 144.29710    67.78781
## 6                     1                     0          0 123.30240    68.69784
## 7                     1                     0          1 141.49470    69.80204
## 8                     1                     1          0 136.46230    70.01472
## 9                     0                     0          0 112.37230    67.90265
## 10                    0                     1          1 120.66720    66.78236
## 11                    1                     1          0 127.45160    66.48769
## 12                    1                     0          1 114.14300    67.62333
## 13                    1                     0          0 125.61070    68.30248
## 14                    1                     0          1 122.46180    67.11656
## 15                    0                     0          1 116.08660    68.27967
## 16                    1                     1          0 139.99750    71.09160
## 17                    1                     0          1 129.50230    66.46100
## 18                    0                     1          1 142.97330    68.64927
## 19                    1                     0          0 137.90250    71.23033
## 20                    1                     0          0 124.04490    67.13118
## 21                    1                     1          0 141.28070    67.83379
## 22                    0                     1          0 143.53920    68.87881
## 23                    1                     0          0  97.90191    63.48115
## 24                    1                     0          1 129.50270    68.42187
## 25                    0                     1          1 141.85010    67.62804
## 26                    1                     1          1 129.72440    67.20864
## 27                    1                     1          1 142.42350    70.84235
## 28                    1                     0          1 131.55020    67.49434
## 29                    1                     1          1 108.33240    66.53401
## 30                    1                     0          0 113.89220    65.44098
## 31                    1                     0          0 103.30160    69.52330
## 32                    1                     1          1 120.75360    65.81320
## 33                    1                     1          0 125.78860    67.81630
## 34                    1                     1          1 136.22250    70.59505
## 35                    0                     1          1 140.10150    71.80484
## 36                    1                     1          0 128.74870    69.20613
## 37                    1                     0          1 141.79940    66.80368
## 38                    1                     1          0 121.23190    67.65893
## 39                    1                     0          1 131.34780    67.80701
## 40                    0                     0          1 106.71150    64.04535
## 41                    1                     0          1 124.35980    68.57463
## 42                    0                     1          0 124.85910    65.18357
## 43                    0                     0          0 139.67110    69.65814
## 44                    1                     0          1 137.36960    67.96731
## 45                    0                     1          0 106.44990    65.98088
## 46                    1                     1          1 128.76390    68.67249
## 47                    1                     1          1 145.68370    66.88088
## 48                    0                     1          1 116.81900    67.69868
## 49                    1                     1          1 143.62150    69.82117
## 50                    0                     0          0 134.93250    69.08817
## 51                    0                     0          1 147.02190    69.91479
## 52                    1                     0          0 126.32850    67.33182
## 53                    0                     1          1 125.48390    70.26939
## 54                    1                     1          1 115.70840    69.10344
## 55                    0                     0          0 123.48920    65.38356
## 56                    0                     1          0 147.89260    70.18447
## 57                    1                     0          1 155.89870    70.40617
## 58                    1                     1          1 128.07420    66.54376
## 59                    1                     1          1 119.37010    66.36418
## 60                    1                     0          1 133.81480    67.53700
## 61                    0                     1          1 128.73250    66.50418
## 62                    0                     0          0 137.54530    68.99958
## 63                    0                     0          0 129.76040    68.30355
## 64                    0                     1          0 128.82400    67.01255
## 65                    1                     0          1 135.31650    70.80592
## 66                    0                     1          1 109.61130    68.21951
## 67                    1                     0          1 142.46840    69.05914
## 68                    1                     0          0 132.74900    67.73103
## 69                    1                     1          1 103.52750    67.21568
## 70                    1                     1          0 124.72990    67.36763
## 71                    0                     1          1 129.31370    65.27033
## 72                    1                     1          0 134.01750    70.84278
## 73                    1                     0          1 140.39690    69.92442
## 74                    1                     0          0 102.83510    64.28508
## 75                    1                     0          1 128.52140    68.24520
## 76                    0                     0          0 120.29910    66.35708
## 77                    1                     1          1 138.60360    68.36275
## 78                    1                     0          1 132.95740    65.47690
## 79                    0                     1          1 115.62330    69.71947
## 80                    1                     1          1 122.52400    67.72554
## 81                    1                     0          0 134.62540    68.63941
## 82                    1                     1          0 121.89860    66.78405
## 83                    0                     1          1 155.37670    70.05147
## 84                    1                     0          0 128.94180    66.27848
## 85                    1                     0          1 129.10130    69.20198
## 86                    1                     1          0 139.47330    69.13481
## 87                    1                     0          1 140.89010    67.36436
## 88                    0                     1          1 131.59160    70.09297
## 89                    0                     0          0 121.12320    70.17660
## 90                    0                     1          1 131.51270    68.22556
## 91                    0                     1          1 136.54790    68.12932
## 92                    1                     0          1 141.48960    70.24256
## 93                    0                     1          1 140.61040    71.48752
## 94                    1                     1          0 112.14130    69.20477
## 95                    1                     1          1 133.45700    70.06306
## 96                    0                     1          1 131.80010    70.55703
## 97                    1                     0          1 120.02850    66.28644
## 98                    1                     0          0 123.09720    63.42577
## 99                    0                     1          0 128.14320    66.76711
## 100                   1                     0          1 115.47590    68.88741
## 101                   0                     0          0 102.09270    64.87434
## 102                   1                     1          1 130.35300    67.09272
## 103                   1                     0          1 134.18420    68.34761
## 104                   0                     1          1  98.64133    65.61073
## 105                   1                     1          1 114.55990    67.75551
## 106                   1                     0          0 123.49170    68.02120
## 107                   1                     1          0 123.04800    67.66193
## 108                   0                     1          1 126.47720    66.31460
## 109                   1                     0          0 128.41700    69.43706
## 110                   1                     0          1 127.19410    63.83624
## 111                   1                     1          1 122.05620    67.72277
## 112                   1                     1          1 127.60640    70.05098
## 113                   1                     0          1 131.64230    70.18602
## 114                   0                     1          1 111.89550    65.94588
## 115                   1                     0          0 122.03900    70.00700
## 116                   1                     0          0 128.55470    68.61129
## 117                   1                     0          1 132.67920    68.80817
## 118                   1                     1          0 136.06320    69.76212
## 119                   1                     1          0 115.94030    65.45539
## 120                   0                     1          1 136.90410    68.82534
## 121                   1                     1          0 119.88040    65.80030
## 122                   1                     0          1 109.00550    67.21474
## 123                   1                     0          0 128.27050    69.42021
## 124                   1                     0          0 135.29130    68.94396
## 125                   0                     0          1 106.85580    67.94150
## 126                   1                     0          0 123.29390    65.62506
## 127                   1                     0          1 109.51430    66.49607
## 128                   0                     1          1 119.30870    67.92809
## 129                   1                     1          0 140.24020    68.89415
## 130                   1                     0          0 133.98410    70.24100
## 131                   1                     1          0 132.58070    68.26623
## 132                   0                     1          0 130.69880    71.23161
## 133                   1                     0          0 115.56370    69.09747
## 134                   1                     0          1 123.79410    64.39693
## 135                   0                     1          1 128.14270    71.09585
## 136                   1                     1          0 135.96460    68.21868
## 137                   1                     0          1 116.62730    65.91721
## 138                   1                     0          1 126.82410    67.43690
## 139                   1                     1          1 151.39130    73.90107
## 140                   1                     0          0 130.40220    69.98149
## 141                   1                     0          0 136.20680    69.51862
## 142                   1                     0          1 113.39890    65.18437
## 143                   1                     1          0 125.32870    68.00869
## 144                   1                     1          1 127.58460    68.33840
## 145                   0                     1          1 107.15640    65.18417
## 146                   1                     1          0 116.45880    68.26209
## 147                   1                     0          1 133.84020    68.56865
## 148                   1                     1          0 112.89010    64.49675
## 149                   1                     0          1 130.75680    68.71053
## 150                   0                     0          1 137.75710    68.89148
## 151                   1                     0          1 125.40360    69.54011
## 152                   0                     1          0 138.46590    67.39964
## 153                   0                     0          0 120.81840    66.47521
## 154                   0                     0          1 140.15390    66.01217
## 155                   0                     0          0 136.73970    72.44434
## 156                   0                     0          1 106.11390    64.12642
## 157                   0                     0          1 158.95620    70.98112
## 158                   0                     0          1 108.78680    67.50124
## 159                   1                     1          1 138.77580    72.01515
## 160                   0                     0          0 115.91360    65.31143
## 161                   0                     0          1 146.29220    67.07509
## 162                   1                     0          0 109.87650    64.39148
## 163                   0                     1          1 139.04990    69.37003
## 164                   1                     1          1 119.90010    68.37921
## 165                   0                     0          0 128.30690    65.31018
## 166                   0                     1          0 127.24280    67.13690
## 167                   1                     0          1 115.23060    68.39468
## 168                   1                     1          1 124.79750    66.29180
## 169                   1                     1          1 126.95110    67.18660
## 170                   1                     0          1 111.27110    65.99156
## 171                   0                     1          1 122.60890    69.43393
## 172                   0                     0          0 124.20840    67.97463
## 173                   0                     0          0 124.64530    67.76133
## 174                   0                     1          0 119.51690    65.27864
## 175                   1                     0          1 139.29830    73.83364
## 176                   0                     1          1 104.82650    66.81312
## 177                   1                     0          1 123.04240    66.89411
## 178                   1                     0          0 118.89230    65.73568
## 179                   1                     1          1 121.49390    65.98283
## 180                   1                     1          0 119.24880    66.58396
## 181                   0                     1          1 135.02390    67.11294
## 182                   1                     1          0 116.22800    65.87481
## 183                   1                     0          1 109.17310    66.78067
## 184                   1                     0          0 124.22370    68.73577
## 185                   1                     0          1 141.16450    66.22666
## 186                   0                     0          0 129.15010    65.95968
## 187                   0                     0          0 127.86930    68.58372
## 188                   0                     0          0 120.92440    66.59347
## 189                   0                     0          0 127.64660    66.96574
## 190                   0                     0          0 101.46930    68.08015
## 191                   0                     0          0 144.99270    70.19025
## 192                   0                     0          0 110.95230    65.52149
## 193                   0                     0          0 132.86250    67.45905
## 194                   0                     0          0 146.33850    67.40985
## 195                   1                     0          1 145.58940    69.66158
## 196                   1                     1          0 120.84310    65.79799
## 197                   1                     0          1 115.78130    66.10558
## 198                   0                     1          1 128.30190    68.23987
## 199                   0                     0          0 127.47180    68.02403
## 200                   0                     1          1 127.87610    71.39044
## 201                   0                     1          1 121.49970    65.73160
## 202                   1                     0          1 112.71480    66.43358
## 203                   0                     1          1 135.00200    70.01309
## 204                   1                     1          0 128.67890    69.48146
## 205                   1                     1          1 124.40620    68.62764
## 206                   0                     1          1 140.02600    68.36275
## 207                   1                     0          1 117.51900    68.39028
## 208                   1                     0          0 143.87370    68.77413
## 209                   0                     1          0 141.17030    69.92360
## 210                   1                     0          1 155.94140    71.55542
## 211                   0                     0          0 134.00930    68.44764
## 212                   1                     1          1 130.09750    66.71398
## 213                   1                     0          1 106.22650    66.68413
## 214                   0                     1          1 112.04890    67.93699
## 215                   1                     1          1 136.18840    68.89855
## 216                   1                     0          0 131.23600    67.29191
## 217                   1                     1          0 131.32310    69.57212
## 218                   0                     1          1 119.52610    67.67479
## 219                   1                     0          0 116.99650    69.04155
## 220                   1                     0          1 138.52550    67.96765
## 221                   1                     1          1 109.65180    65.83982
## 222                   0                     0          0 130.15690    65.77288
## 223                   0                     0          1 137.11140    71.14106
## 224                   1                     0          0 113.75900    67.83055
## 225                   0                     1          1 114.97250    65.06930
## 226                   1                     1          1 127.71490    69.70745
## 227                   0                     0          0 121.99720    69.92983
## 228                   0                     1          0 117.96070    66.11569
## 229                   1                     0          1 127.71410    68.61364
## 230                   1                     1          1 117.96190    68.99760
## 231                   1                     1          1 125.15540    66.79171
## 232                   1                     0          1 141.10260    68.02363
## 233                   0                     1          1 145.48220    69.67258
## 234                   0                     0          0 116.06500    71.82178
## 235                   0                     0          0 135.74580    72.74676
## 236                   0                     1          0 132.92480    67.27951
## 237                   1                     0          1 115.66220    67.41015
## 238                   0                     1          1 114.31840    68.53150
## 239                   1                     0          1 148.95200    68.47126
## 240                   0                     1          0 142.18780    68.51867
## 241                   1                     0          0 134.10400    63.72529
## 242                   1                     0          1 141.89260    67.70483
## 243                   0                     1          1 138.74440    69.47115
## 244                   1                     1          0 134.44900    66.70198
## 245                   1                     0          1 117.01670    65.23126
## 246                   1                     0          1 115.67520    69.89473
## 247                   1                     1          1 134.79050    69.83048
## 248                   1                     0          0 120.57460    65.39790
## 249                   1                     0          0 120.08350    68.32214
## 250                   0                     0          0  84.35980    65.93895
## 251                   1                     1          0 138.93940    70.09805
## 252                   1                     1          1 143.52450    66.05531
## 253                   0                     1          1 123.13470    68.23481
## 254                   1                     1          0 115.52610    65.21758
## 255                   1                     0          1 120.98440    69.16173
## 256                   1                     1          0 120.64730    67.60064
## 257                   1                     0          1 124.03520    67.28621
## 258                   0                     0          1 117.22380    66.84323
## 259                   1                     0          1 127.95980    68.08281
## 260                   0                     1          0 116.75270    66.56991
## 261                   0                     0          0 121.99570    70.16973
## 262                   1                     0          1 123.99520    67.85113
## 263                   1                     0          0 108.85500    66.62309
## 264                   1                     0          0 104.65740    63.68816
## 265                   1                     0          1 132.24800    68.03560
## 266                   1                     1          0 127.18340    66.94100
## 267                   0                     0          0 125.12090    66.26292
## 268                   0                     1          1 133.32200    70.73010
## 269                   1                     1          0 122.33640    70.70844
## 270                   1                     0          1 130.26360    73.26872
## 271                   1                     0          0 116.74310    63.79021
## 272                   1                     0          1 125.85340    67.84109
## 273                   0                     0          1 100.62700    67.78058
## 274                   1                     1          0 118.49450    67.23901
## 275                   1                     0          1 137.12550    66.75701
## 276                   0                     1          1 118.69910    69.03098
## 277                   1                     0          0 124.16410    68.52652
## 278                   1                     0          0 124.94420    64.65419
## 279                   1                     1          0 126.38890    65.14295
## 280                   0                     1          0 121.52550    66.74124
## 281                   1                     0          0 133.29510    66.99923
## 282                   1                     0          1 127.40720    70.26611
## 283                   0                     1          1 125.08000    67.57666
## 284                   1                     1          1 102.81140    66.30582
## 285                   0                     1          1 134.22120    68.90702
## 286                   1                     1          0 100.97580    65.60543
## 287                   1                     0          0 145.88860    68.00189
## 288                   1                     1          0 155.30460    69.93715
## 289                   0                     1          0 138.71750    70.14590
## 290                   1                     0          0 116.26110    66.66364
## 291                   1                     0          1 120.60870    69.40676
## 292                   0                     1          1 114.40830    66.80598
## 293                   1                     1          0 133.34060    67.70048
## 294                   1                     0          1  92.74955    69.13438
## 295                   1                     0          1 131.78250    67.53769
## 296                   1                     1          1 118.38650    65.77912
## 297                   1                     0          0 131.14660    66.25769
## 298                   1                     0          0 130.20330    67.39038
## 299                   1                     0          1 129.18360    64.94327
## 300                   1                     1          0 143.14450    69.25699
## 301                   1                     1          1 138.73070    69.07739
## 302                   0                     1          1 130.95280    69.64403
## 303                   1                     1          0 124.30320    69.07705
## 304                   1                     0          1 135.37020    68.01304
## 305                   1                     1          0 124.19880    68.85664
## 306                   1                     0          1 111.23890    63.19158
## 307                   0                     0          1 129.40370    65.57591
## 308                   1                     0          1 127.74440    69.12101
## 309                   0                     1          0 121.33110    69.78765
matstd.lung <- scale(lung)
lung_scaled <- scale(lung)
attach(lung)
## The following objects are masked from data:
## 
##     AGE, ALCOHOL_CONSUMING, ALLERGY, ANXIETY, CHEST_PAIN,
##     CHRONIC_DISEASE, COUGHING, FATIGUE, GENDER, HEIGHT_INCH,
##     LUNG_CANCER, PEER_PRESSURE, SHORTNESS_OF_BREATH, SMOKING,
##     SWALLOWING_DIFFICULTY, WEIGHT, WHEEZING, YELLOW_FINGERS
## The following objects are masked from cancer (pos = 31):
## 
##     AGE, ALCOHOL_CONSUMING, ALLERGY, ANXIETY, CHEST_PAIN,
##     CHRONIC_DISEASE, COUGHING, FATIGUE, GENDER, HEIGHT_INCH,
##     LUNG_CANCER, PEER_PRESSURE, SHORTNESS_OF_BREATH, SMOKING,
##     SWALLOWING_DIFFICULTY, WEIGHT, WHEEZING, YELLOW_FINGERS
## The following objects are masked from cancer (pos = 51):
## 
##     AGE, ALCOHOL_CONSUMING, ALLERGY, ANXIETY, CHEST_PAIN,
##     CHRONIC_DISEASE, COUGHING, FATIGUE, GENDER, HEIGHT_INCH,
##     LUNG_CANCER, PEER_PRESSURE, SHORTNESS_OF_BREATH, SMOKING,
##     SWALLOWING_DIFFICULTY, WEIGHT, WHEEZING, YELLOW_FINGERS
dim(lung)
## [1] 309  18
str(lung)
## 'data.frame':    309 obs. of  18 variables:
##  $ LUNG_CANCER          : int  1 1 0 0 0 1 1 1 0 1 ...
##  $ GENDER               : int  0 0 1 0 1 1 0 1 1 0 ...
##  $ AGE                  : int  69 74 59 63 63 75 52 51 68 53 ...
##  $ SMOKING              : int  1 0 1 0 1 1 0 0 0 0 ...
##  $ YELLOW_FINGERS       : int  1 0 0 1 1 1 0 1 0 1 ...
##  $ ANXIETY              : int  1 0 0 1 0 0 0 1 1 1 ...
##  $ PEER_PRESSURE        : int  0 0 1 0 0 0 0 1 0 1 ...
##  $ CHRONIC_DISEASE      : int  0 1 0 0 0 1 0 0 0 1 ...
##  $ FATIGUE              : int  1 1 1 0 0 1 1 1 1 0 ...
##  $ ALLERGY              : int  0 1 0 0 0 1 0 1 0 1 ...
##  $ WHEEZING             : int  1 0 1 0 1 1 1 0 0 0 ...
##  $ ALCOHOL_CONSUMING    : int  1 0 0 1 0 0 1 0 0 1 ...
##  $ COUGHING             : int  1 0 1 0 1 1 1 0 0 0 ...
##  $ SHORTNESS_OF_BREATH  : int  1 1 1 0 1 1 1 1 0 0 ...
##  $ SWALLOWING_DIFFICULTY: int  1 1 0 1 0 0 0 1 0 1 ...
##  $ CHEST_PAIN           : int  1 1 1 1 0 0 1 0 0 1 ...
##  $ WEIGHT               : num  113 136 153 142 144 ...
##  $ HEIGHT_INCH          : num  65.8 71.5 69.4 68.2 67.8 ...
lung$LUNG_CANCER <- as.factor(lung$LUNG_CANCER)
str(lung)
## 'data.frame':    309 obs. of  18 variables:
##  $ LUNG_CANCER          : Factor w/ 2 levels "0","1": 2 2 1 1 1 2 2 2 1 2 ...
##  $ GENDER               : int  0 0 1 0 1 1 0 1 1 0 ...
##  $ AGE                  : int  69 74 59 63 63 75 52 51 68 53 ...
##  $ SMOKING              : int  1 0 1 0 1 1 0 0 0 0 ...
##  $ YELLOW_FINGERS       : int  1 0 0 1 1 1 0 1 0 1 ...
##  $ ANXIETY              : int  1 0 0 1 0 0 0 1 1 1 ...
##  $ PEER_PRESSURE        : int  0 0 1 0 0 0 0 1 0 1 ...
##  $ CHRONIC_DISEASE      : int  0 1 0 0 0 1 0 0 0 1 ...
##  $ FATIGUE              : int  1 1 1 0 0 1 1 1 1 0 ...
##  $ ALLERGY              : int  0 1 0 0 0 1 0 1 0 1 ...
##  $ WHEEZING             : int  1 0 1 0 1 1 1 0 0 0 ...
##  $ ALCOHOL_CONSUMING    : int  1 0 0 1 0 0 1 0 0 1 ...
##  $ COUGHING             : int  1 0 1 0 1 1 1 0 0 0 ...
##  $ SHORTNESS_OF_BREATH  : int  1 1 1 0 1 1 1 1 0 0 ...
##  $ SWALLOWING_DIFFICULTY: int  1 1 0 1 0 0 0 1 0 1 ...
##  $ CHEST_PAIN           : int  1 1 1 1 0 0 1 0 0 1 ...
##  $ WEIGHT               : num  113 136 153 142 144 ...
##  $ HEIGHT_INCH          : num  65.8 71.5 69.4 68.2 67.8 ...
# Lets see what the optimal numbers of clusers are
# Compute
res.nbclust <- lung_scaled %>% scale() %>% NbClust(distance = "euclidean", min.nc = 2, max.nc = 10, method = "complete", index ="all") 

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 7 proposed 2 as the best number of clusters 
## * 1 proposed 3 as the best number of clusters 
## * 2 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 6 as the best number of clusters 
## * 7 proposed 7 as the best number of clusters 
## * 1 proposed 8 as the best number of clusters 
## * 3 proposed 10 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  2 
##  
##  
## *******************************************************************
# Perform k-means clustering with 3 clusters
set.seed(123)
k3 <- kmeans(lung_scaled, centers = 3, nstart = 25)

# Visualize the clustering results with a scatter plot
fviz_cluster(k3, data = lung_scaled)

# Determine the optimal number of clusters using the elbow method
fviz_nbclust(lung_scaled, kmeans, method = "wss")

# Assign cluster labels to the original dataset
lung$cluster <- as.factor(k3$cluster)
lung$cluster
##   [1] 3 3 1 1 1 3 3 2 1 2 2 3 1 3 3 2 3 2 2 1 2 2 1 3 2 3 2 1 2 1 1 3 1 2 1 2 3
##  [38] 1 3 3 3 3 2 3 2 2 3 2 2 1 3 2 3 3 2 2 2 3 2 3 3 1 3 2 3 2 3 3 2 2 2 2 3 1
##  [75] 3 3 2 3 2 2 1 2 2 3 3 2 3 2 2 2 2 3 3 2 3 2 2 3 2 3 3 2 3 2 2 1 2 2 3 3 3
## [112] 2 3 2 3 3 3 2 2 2 2 3 1 2 3 2 3 2 2 1 2 2 1 3 2 3 2 3 2 3 2 3 2 2 2 2 3 2
## [149] 3 3 3 3 2 1 1 2 1 1 2 1 3 2 3 3 2 2 2 3 2 3 3 1 3 2 3 2 3 3 2 2 2 2 3 1 3
## [186] 3 2 1 2 2 1 2 2 1 3 2 3 2 2 2 2 3 3 2 3 2 2 1 2 3 3 2 3 2 2 1 2 2 3 3 2 1
## [223] 3 2 3 3 2 2 2 3 2 3 3 2 3 2 3 2 3 2 1 3 2 3 2 1 2 3 2 1 2 2 2 2 3 2 3 3 3
## [260] 3 2 3 1 3 3 2 1 2 2 3 1 3 3 2 3 2 2 1 2 2 1 1 1 3 2 2 1 2 2 1 3 2 3 2 3 2
## [297] 3 2 3 2 2 2 2 3 2 3 3 3 3
## Levels: 1 2 3
# Hierarchial Clusiering
res.hc <- lung_scaled %>% scale() %>% dist(method = "euclidean") %>%
  hclust(method = "ward.D2")

fviz_dend(res.hc, k = 3, # Cut in three groups
          cex = 0.5, # label size
          k_colors = c("#2E9FDF", "#E7B800", "#FC4E07"),
          color_labels_by_k = TRUE, # color labels by groups
          rect = TRUE # Add rectangle around groups
          )
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
##   Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.